Signal processing apparatus and method

ABSTRACT

A signal processor which acquires a first signal, including a first desired signal portion and a first undesired signal portion, and a second signal, including a second desired signal portion and a second undesired signal portion, wherein the first and second desired signal portions are correlated. The signals may be acquired by propagating energy through a medium and measuring an attenuated signal after transmission or reflection. Alternatively, the signals may be acquired by measuring energy generated by the medium. A processor generates a noise reference signal which is a combination of only the undesired signal portions and is correlated to both the first and second undesired signal portions. The noise reference signal is then used to remove the undesired portion of each of the first and second measured signals via an adaptive noise canceler, preferably of the joint process estimator type. The processor may be employed in conjunction with an adaptive noise canceler in physiological monitors wherein the know properties of energy attenuation through a medium are used to determine physiological characteristics of the medium. Many physiological conditions, such as the pulse of a patient or the concentration of a constituent in a medium, can be determined from the desired portion of the signal after undesired signal portions, such as those caused by erratic motion, are removed.

The present application is a continuation of application Ser. No.08/479,918, now U.S. Pat. No. 5,769,785, filed Jun. 7, 1995, which is acontinuation of application Ser. No. 08/249,690, now U.S. Pat. No.5,482,036, filed May 26, 1994, which is a continuation of applicationSer. No. 07/666,060 filed Mar. 7, 1991, now abandoned.

FIELD OF THE INVENTION

The present invention relates to the field of signal processing. Morespecifically, the present invention relates to the processing ofmeasured signals to remove undesired portions when little is known aboutthe undesired signal portion.

BACKGROUND OF THE INVENTION

Signal processors are typically employed to remove undesired portionsfrom a composite measured signal including a desired signal portion andan undesired signal portion. If the undesired signal portion occupies adifferent frequency spectrum than the desired signal, then conventionalfiltering techniques such as low pass, band pass, and high passfiltering could be used to separate the desired portion from the totalsignal. Fixed single or multiple notch filters could also be employed ifthe undesired signal portion(s) exist at a fixed frequency(s).

However, it is often the case that an overlap in frequency spectrumbetween the desired and undesired signal portions does exist and thestatistical properties of both signal portions change with time. In suchcases, conventional filtering techniques are totally ineffective inextracting the desired signal. If, however, a description of theundesired portion can be made available, adaptive noise canceling can beemployed to remove the undesired portion of the signal leaving thedesired portion available for measurement. Adaptive noise cancelersdynamically change their transfer function to adapt to and remove theundesired signal portions of a composite signal. Adaptive noisecancelers require a noise reference signal which is correlated to theundesired signal portion. The noise reference signal is not necessarilya representation of the undesired signal portion, but has a frequencyspectrum which is similar to that of the undesired signal. In manycases, it requires considerable ingenuity to determine a noise referencesignal since nothing is a priori known about the undesired signalportion.

One area where composite measured signals comprise a desired signalportion and an undesired signal portion about which no information caneasily be determined is physiological monitoring. Physiologicalmonitoring apparatuses generally measure signals derived from aphysiological system, such as the human body. Measurements which aretypically taken with physiological monitoring systems include electroncardiographs, blood pressure, blood gas saturation (such as oxygensaturation), capnographs, heart rate, respiration rate, and depth ofanesthesia, for example. Other types of measurements include those whichmeasure the pressure and quantity of a substance within the body such asbreathalizer testing, drug testing, cholesterol testing, glucosetesting, arterial carbon dioxide testing, protein testing, and carbonmonoxide testing, for example. The source of the undesired signalportion in these measurements is often due to motion of the patient,both external and internal (muscle movement, for example), during themeasurement process.

Knowledge of physiological systems, such as the amount of oxygen in apatient's blood, can be critical, for example during surgery. Data canbe determined by a lengthy invasive procedure of extracting and testingmatter, such as blood, from a patient, or by more expedient,non-invasive measures. Many types of non-invasive measurements can bemade by using the known properties of energy attenuation as a selectedform of energy passes through a medium.

Energy is caused to be incident on a medium either derived from orcontained within a patient and the amplitude of transmitted or reflectedenergy is then measured. The amount of attenuation of the incidentenergy caused by the medium is strongly dependent on the thickness andcomposition of the medium through which the energy must pass as well asthe specific form of energy selected. Information about a physiologicalsystem can be derived from data taken from the attenuated signal of theincident energy transmitted through the medium if the noise can beremoved. However, non-invasive measurements often do not afford theopportunity to selectively observe the interference causing theundesired signal portion, making it difficult to remove.

These undesired signal portions often originate from both AC and DCsources. The first undesired portion is an easily removed DC componentcaused by transmission of the energy through differing media which areof relatively constant thickness within the body, such as bone, tissue,skin, blood, etc. Second, is an erratic AC component caused whendiffering media being measured are perturbed and thus, change inthickness while the measurement is being made. Since most materials inand derived from the body are easily compressed, the thickness of suchmatter changes if the patient moves during a non-invasive physiologicalmeasurement. Patient movement can cause the properties of energyattenuation to vary erratically. Traditional signal filtering techniquesare frequently totally ineffective and grossly deficient in removingthese motion induced effects from a signal. The erratic or unpredictablenature of motion induced undesired signal components is the majorobstacle in removing them. Thus, presently available physiologicalmonitors generally become totally inoperative during time periods whenthe patient moves.

A blood gas monitor is one example of a physiological monitoring systemwhich is based upon the measurement of energy attenuated by biologicaltissues or substances. Blood gas monitors transmit light into the tissueand measure the attenuation of the light as a function of time. Theoutput signal of a blood gas monitor which is sensitive to the arterialblood flow contains a component which is a waveform representative ofthe patient's arterial pulse. This type of signal, which contains acomponent related to the patient's pulse, is called a plethysmographicwave, and is shown in FIG. 1 as curve Y. Plethysmographic waveforms areused in blood pressure or blood gas saturation measurements, forexample. As the heart beats the amount of blood in the arteriesincreases and decreases, causing increases and decreases in energyattenuation, illustrated by the cyclic wave Y in FIG. 1.

Typically, a digit such as a finger, an ear lobe, or other portion ofthe body where blood flows close to the skin, is employed as the mediumthrough which light energy is transmitted for blood gas attenuationmeasurements. The finger comprises skin, fat, bone, muscle, etc., shownschematically in FIG. 2, each of which attenuates energy incident on thefinger in a generally predictable and constant manner. However, whenfleshy portions of the finger are compressed erratically, for example bymotion of the finger, energy attenuation becomes erratic.

An example of a more realistic measured waveform S is shown in FIG. 3,illustrating the effect of motion. The desired portion of the signal Yis the waveform representative of the pulse, corresponding to thesawtooth-like pattern wave in FIG. 1. The large, motion-inducedexcursions in signal amplitude hide the desired signal Y. It is easy tosee how even small variations in amplitude make it difficult todistinguish the desired signal Y in the presence of a noise component n.

A specific example of a blood gas monitoring apparatus is a pulseoximeter which measures the saturation of oxygen in the blood. Thepumping of the heart forces freshly oxygenated blood into the arteriescausing greater energy attenuation. The saturation of oxygenated bloodmay be determined from the depth of the valleys relative to the peaks oftwo plethysmographic waveforms measured at separate wavelengths.However, motion induced undesired signal portions, or motion artifacts,must be removed from the measured signal for the oximeter to continuethe measurement during periods when the patient moves.

SUMMARY OF THE INVENTION

The present invention is a signal processor which acquires a firstsignal and a second signal that is correlated to the first signal. Thefirst signal comprises a first desired signal portion and a firstundesired signal portion. The second signal comprises a second desiredsignal portion and a second undesired signal portion. The signals may beacquired by propagating energy through a medium and measuring anattenuated signal after transmission or reflection. Alternatively, thesignal may be acquired by measuring energy generated by the medium.

The first and second measured signals are processed to generate a noisereference signal which does not contain the desired signal portions fromeither of the first or second measured signals. The remaining undesiredsignal portions from the first and second measured signals are combinedto form a noise reference signal. This noise reference signal iscorrelated to the undesired signal portion of each of the first andsecond measured signals.

The noise reference signal is then used to remove the undesired portionof each of the first and second measured signals via an adaptive noisecanceler. An adaptive noise canceler can be described by analogy to adynamic multiple notch filter which dynamically changes its transferfunction in response to the noise reference signal and the measuredsignals to remove frequencies from the measured signals that are alsopresent in the noise reference signal. Thus, a typical adaptive noisecanceler receives the signal from which it is desired to remove noiseand a noise reference signal. The output of the adaptive noise canceleris a good approximation to the desired signal with the noise removed.

Physiological monitors can often advantageously employ signal processorsof the present invention. Often in physiological measurements a firstsignal comprising a first desired portion and a first undesired portionand a second signal comprising a second desired portion and a secondundesired portion are acquired. The signals may be acquired bypropagating energy through a patient's body (or a material which isderived from the body, such as breath, blood, or tissue, for example)and measuring an attenuated signal after transmission or reflection.Alternatively, the signal may be acquired by measuring energy generatedby a patient's body, such as in electrocardiography. The signals areprocessed via the signal processor of the present invention to acquire anoise reference signal which is input to an adaptive noise canceler.

One physiological monitoring apparatus which can advantageouslyincorporate the features of the present invention is a monitoring systemwhich determines a signal which is representative of the arterial pulse,called a plethysmographic wave. This signal can be used in bloodpressure calculations, blood gas saturation measurements, etc. Aspecific example of such a use is in pulse oximetry which determines thesaturation of oxygen in the blood. In this configuration, the desiredportion of the signal is the arterial blood contribution to attenuationof energy as it passes through a portion of the body where blood flowsclose to the skin. The pumping of the heart causes blood flow toincrease and decrease in the arteries in a periodic fashion, causingperiodic attenuation wherein the periodic waveform is theplethysmographic waveform representative of the pulse.

A physiological monitor particularly adapted to pulse oximetry oxygensaturation measurement comprises two light emitting diodes (LED's) whichemit light at different wavelengths to produce first and second signals.A detector registers the attenuation of the two different energy signalsafter each passes through an absorptive media, for example a digit suchas a finger, or an earlobe. The attenuated signals generally compriseboth desired and undesired signal portions. A static filtering system,such as a band pass filter, removes a portion of the undesired signalwhich is static, or constant, or outside of a known bandwidth ofinterest, leaving an erratic or random undesired signal portion, oftencaused by motion and often difficult to remove, along with the desiredsignal portion.

Next, a processor of the present invention removes the desired signalportions from the measured signals yielding a noise reference signalwhich is a combination of the remaining undesired signal portions. Thenoise reference signal is correlated to both of the undesired signalportions. The noise reference signal and at least one of the measuredsignals are input to an adaptive noise canceler which removes the randomor erratic portion of the undesired signal. This yields a goodapproximation to the desired plethysmographic signal as measured at oneof the measured signal wavelengths. As is known in the art, quantitativemeasurements of the amount of oxygenated blood in the body can bedetermined from the plethysmographic signal in a variety of ways.

One aspect of the present invention is a signal processor comprising adetector for receiving a first signal which travels along a firstpropagation path and a second signal which travels along a secondpropagation path wherein a portion of the first and second propagationpaths are located in a propagation medium. The first signal has a firstdesired signal portion and a first undesired signal portion and thesecond signal has a second desired signal portion and a second undesiredsignal portion. The first and second undesired signal portions are aresult of a perturbation of the propagation medium. This aspect of theinvention additionally comprises a reference processor having an inputfor receiving the first and second signals. The processor is adapted tocombine the first and second signals to generate a reference signalhaving a primary component which is a function of the first and saidsecond undesired signal portions.

The above described aspect of the present invention may further comprisean adaptive signal processor for receiving the reference signal and thefirst signal and for deriving therefrom an output signal having aprimary component which is a function of the first desired signalportion of the first signal. Alternatively, the above described aspectof the present invention may further comprise an adaptive signalprocessor for receiving the reference signal and the second signal andfor deriving therefrom an output signal having a primary component whichis a function of the second desired signal portion of the second signal.The adaptive signal processor may comprise an adaptive noise canceler.The adaptive noise canceler may be comprise a joint process estimatorhaving a least-squares-lattice predictor and a regression filter.

The detector in the aspect of the signal processor of the presentinvention described above may further comprise a sensor for sensing aphysiological function. The sensor may comprise a light sensitivedevice. Additionally, the present invention may further comprising apulse oximeter for measuring oxygen saturation in a living organism.

Another aspect of the present invention is a physiological monitoringapparatus comprising a detector for receiving a first physiologicalmeasurement signal which travels along a first propagation path and asecond physiological measurement signal which travels along a secondpropagation path. A portion of the first and second propagation paths islocated in a propagation medium. The first signal has a first desiredsignal portion and a first undesired signal portion and the secondsignal has a second desired signal portion and a second undesired signalportion. The physiological monitoring apparatus further comprises areference processor having an input for receiving the first and secondsignals. The processor is adapted to combine the first and secondsignals to generate a reference signal having a primary component whichis a function of the first and the second undesired signal portions.

The physiological monitoring apparatus may further comprise an adaptivesignal processor for receiving the reference signal and the first signalfor deriving therefrom an output signal having a primary component whichis a function of the first desired signal portion of the first signal.Alternatively, the physiological monitoring apparatus may furthercomprise an adaptive signal processor for receiving the reference signaland the second signal and for deriving therefrom an output signal havinga primary component which is a function of the second desired signalportion of the second signal. The physiological monitoring apparatus mayfurther comprise a pulse oximeter.

A further aspect of the present invention is an apparatus for measuringa blood constituent comprising an energy source for directing aplurality of predetermined wavelengths of electromagnetic energy upon aspecimen and a detector for receiving the plurality of predeterminedwavelengths of electromagnetic energy from the specimen. The detectorproduces electrical signals corresponding to the predeterminedwavelengths in response to the electromagnetic energy. At least two ofthe electrical signals each has a desired signal portion and anundesired signal portion. Additionally, the apparatus comprises areference processor having an input for receiving the electricalsignals. The processor is configured to combine said electrical signalsto generate a reference signal having a primary component which isderived from the undesired signal portions.

This aspect of the present invention may further comprise an adaptivesignal processor for receiving the reference signal and one of the twoelectrical signals and for deriving therefrom an output signal having aprimary component which is a function of the desired signal portion ofthe electrical signal. This may be accomplished by use of an adaptivenoise canceler in the adaptive signal processor which may employ a jointprocess estimator having a least-squares-lattice predictor and aregression filter.

Yet another aspect of the present invention is a blood gas monitor fornon-invasively measuring a blood constituent in a body comprising alight source for directing at least two predetermined wavelengths oflight upon a body and a detector for receiving the light from the body.The detector, in response to the light from the body, produces at leasttwo electrical signals corresponding to the at least two predeterminedwavelengths of light. The at least two electrical signals each has adesired signal portion and an undesired signal portion. The bloodoximeter further comprises a reference processor having an input forreceiving the at least two electrical signals. The processor is adaptedto combine the at least two electrical signals to generate a referencesignal with a primary component which is derived from the undesiredsignal portions. The blood oximeter may further comprise an adaptivesignal processor for receiving the reference signal and the twoelectrical signals and for deriving therefrom at least two outputsignals which are substantially equal, respectively, to the desiredsignal portions of the electrical signals.

The present invention also includes a method of determining a noisereference signal from a first signal comprising a first desired signalportion and a first noise portion and a second signal comprising asecond desired signal portion and a second noise portion. The methodcomprises the steps of selecting a signal coefficient which isproportional to a ratio of predetermined attributes of the first desiredsignal portion and predetermined attributes of the second desired signalportion. The first signal and the second signal coefficient are inputinto a signal multiplier wherein the first signal is multiplied by thesignal coefficient thereby generating a first intermediate signal. Thesecond signal and the first intermediate signal are input into a signalsubtractor wherein the first intermediate signal is subtracted from thesecond signal. This generates a noise reference signal having a primarycomponent which is derived from the first and second noise signalportions. The first and second signals in this method may be derivedfrom light energy transmitted through an absorbing medium.

The present invention further embodies a physiological monitoringapparatus comprising means for acquiring a first signal comprising afirst desired signal portion and a first undesired signal portion and asecond signal comprising a second desired signal portion and a secondundesired signal portion. The physiological monitoring apparatus of thepresent invention also comprises means for determining from the firstand second signals a noise reference signal. Additionally, themonitoring apparatus comprises an adaptive noise canceler having a noisereference input for receiving the noise reference signal and a signalinput for receiving the first signal wherein the adaptive noisecanceler, in real or near real time, generates an output signal whichapproximates the first desired signal portion. The adaptive noisecanceler may further comprise a joint process estimator.

A further aspect of the present invention is an apparatus for processingan amplitude modulated signal having a signal amplitude complicatingfeature, the apparatus comprising an energy source for directingelectromagnetic energy upon a specimen. Additionally, the apparatuscomprises a detector for acquiring a first amplitude modulated signaland a second amplitude modulated signal. Each of the first and secondsignals has a component containing information about the attenuation ofelectromagnetic energy by the specimen and a signal amplitudecomplicating feature. The apparatus includes a reference processor forreceiving the first and second amplitude modulated signals and derivingtherefrom a noise reference signal which is correlated with the signalamplitude complicating feature. Further, the apparatus incorporates anadaptive noise canceler having a signal input for receiving the firstamplitude modulated signal, a noise reference input for receiving thenoise reference signal, wherein the adaptive noise canceler produces anoutput signal having a primary component which is derived from thecomponent containing information about the attenuation ofelectromagnetic energy by the specimen.

Still another aspect of the present invention is an apparatus forextracting a plethysmographic waveform from an amplitude modulatedsignal having a signal amplitude complicating feature, the apparatuscomprising a light source for transmitting light into an organism and adetector for monitoring light from the organism. The detector produces afirst light attenuation signal and a second light attenuation signal,wherein each of the first and second light attenuation signals has acomponent which is representative of a plethysmographic waveform and acomponent which is representative of the signal amplitude complicatingfeature. The apparatus also includes a reference processor for receivingthe first and second light attenuation signals and deriving therefrom anoise reference signal. The noise reference signal and the signalamplitude complicating feature each has a frequency spectrum. Thefrequency spectrum of the noise reference signal is correlated with thefrequency spectrum of the signal amplitude complicating feature.Additionally incorporated into this embodiment of the present inventionis an adaptive noise canceler having a signal input for receiving thefirst attenuation signal and a noise reference input for receiving thenoise reference signal. The adaptive noise canceler produces an outputsignal having a primary component which is derived from the componentwhich is representative of a plethysmographic waveform.

The present invention also comprises a method of removing a motionartifact signal from a signal derived from a physiological measurementwherein a first signal having a physiological measurement component anda motion artifact component and a second signal having a physiologicalmeasurement component and a motion artifact component are acquired. Fromthe first and second signals a motion artifact noise reference signalwhich is a primary function of the first and second signals motionartifact components is derived. This method of removing a motionartifact signal from a signal derived from a physiological measurementmay also comprise the step of inputting the motion artifact noisereference signal into an adaptive noise canceler to produce an outputsignal which is a primary function of the first signal physiologicalmeasurement component.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an ideal plethysmographic waveform.

FIG. 2 schematically illustrates the cross-sectional structure of atypical finger.

FIG. 3 illustrates a plethysmographic waveform which includes amotion-induced undesired erratic signal portion.

FIG. 4 illustrates a schematic diagram of a physiological monitorincorporating a processor of the present invention and an adaptive noisecanceler.

FIG. 4a illustrates the transfer function of a multiple notch filter.

FIG. 5 illustrates an example of an adaptive noise canceler which couldbe employed in a physiological monitor which also incorporates theprocessor of the present invention.

FIG. 6a illustrates a schematic absorbing material comprising Nconstituents within an absorbing material.

FIG. 6b illustrates another schematic absorbing material comprising Nconstituents within an absorbing material.

FIG. 7 is a schematic model of a joint process estimator comprising aleast-squares lattice predictor and a regression filter.

FIG. 8 is a flowchart representing a subroutine capable of implementinga joint process estimator as modeled in FIG. 7.

FIG. 9 is a schematic model of a joint process estimator with aleast-squares lattice predictor and two regression filters.

FIG. 10 is an example of a physiological monitor incorporating aprocessor of the present invention and an adaptive noise canceler withina microprocessor. This physiological monitor is specifically designed tomeasure a plethysmographic waveform and perform pulse oximetrymeasurements.

FIG. 11 is a graph of oxygenated and deoxygenated absorptioncoefficients vs. wavelength.

FIG. 12 is a graph of the ratio of the absorption coefficients ofdeoxygenated hemoglobin divided by oxygenated hemoglobin vs. wavelength.

FIG. 13 is an expanded view of a portion of FIG. 11 marked by a circlelabelled 13.

FIG. 14 illustrates a signal measured at a first red wavelengthλa=λred1=650 nm for use in a processor of the present inventionemploying the ratiometric method for determining the noise referencesignal n′(t) and for use in a joint processor estimator. The measuredsignal comprises a desired portion Y_(λa)(t) and an undesired portionn_(λa)(t).

FIG. 15 illustrates a signal measured at a second red wavelengthλb=λred2=685 nm for use in a processor of the present inventionemploying the ratiometric method for determining the noise referencesignal n′(t). The measured signal comprises a desired portion Y_(λb)(t)and an undesired portion n_(λb)(t).

FIG. 16 illustrates a signal measured at an infrared wavelengthλc=λIR=940 nm for use in a joint process estimator. The measured signalcomprises a desired portion Y_(λc)(t) and an undesired portionn_(λc)(t).

FIG. 17 illustrates the noise reference signal n′(t) determined by aprocessor of the present invention using the ratiometric method.

FIG. 18 illustrates a good approximation Y′_(λa)(t) to the desiredportion Y_(λa)(t) of the signal S_(λa)(t) measured at λa=λred1=650 nmestimated with a noise reference signal n′(t) determined by theratiometric method.

FIG. 19 illustrates a good approximation Y′_(λc)(t) to the desiredportion Y_(λc)(t) of the signal S_(λc)(t) measured at λc=λIR=940 nmestimated with a noise reference signal n′(t) determined by theratiometric method.

FIG. 20 illustrates a signal measured at a red wavelength λa=λred=660 nmfor use in a processor of the present invention employing the constantsaturation method for determining the noise reference signal n′(t) andfor use in a joint process estimator. The measured signal comprises adesired portion Y_(λa)(t) and an undesired portion n_(λa)(t).

FIG. 21 illustrates a signal measured at an infrared wavelengthλb=λIR=940 nm for use in a processor of the present invention employingthe constant saturation method for determining the noise referencesignal n′(t) and for use in a joint process estimator. The measuredsignal comprises a desired portion Y_(λb)(t) and an undesired portionn_(λb)(t).

FIG. 22 illustrates the noise reference signal n′(t) determined by aprocessor of the present invention using the constant saturation method.

FIG. 23 illustrates a good approximation Y′_(λa)(t) to the desiredportion Y_(λa)(t) of the signal S_(λa)(t) measured at λa=λred=660 nmestimated with a noise reference signal n′(t) determined by the constantsaturation method.

FIG. 24 illustrates a good approximation Y′_(λb)(t) to the desiredportion Y_(λb)(t) of the signal S_(λb)(t) measured at λb=λIR=940 nmestimated with a noise reference signal n′(t) determined by the constantsaturation method.

DETAILED DESCRIPTION OF THE INVENTION

The present invention is a processor which determines a noise referencesignal n′(t) for use in an adaptive noise canceler. An adaptive noisecanceler estimates a good approximation Y′(t) to a desired signal Y(t)from a composite signal S(t)=Y(t)+n(t) which, in addition to the desiredportion Y(t) comprises an undesired portion n(t). The undesired portionn(t) may contain one or more of a constant portion, a predictableportion, an erratic portion, a random portion, etc. The approximation tothe desired signal Y′(t) is derived by removing as many of the undesiredportions n(t) from the composite signal S(t) as possible. The constantportion and predictable portion are easily removed with traditionalfiltering techniques, such as simple subtraction, low pass, band pass,and high pass filtering. The erratic portion is more difficult to removedue to its unpredictable nature. If something is known about the erraticsignal, even statistically, it could be removed from the measured signalvia traditional filtering techniques. However, it is often the case thatno information is known about the erratic portion of the noise. In thiscase, traditional filtering techniques are usually insufficient. Oftenno information about the erratic portion of the measured signal isknown. Thus, an adaptive noise canceler is utilized in the presentinvention to remove the erratic portion.

Generally, an adaptive noise canceler has two signal inputs and oneoutput. One of the inputs is the noise reference signal n′(t) which iscorrelated to the erratic undesired signal positions n(t) present in thecomposite signal S(t). The other input is for the composite signal S(t).Ideally, the output of the adaptive noise canceler Y′(t) corresponds tothe desired signal portion Y(t) only. Often, the most difficult task inthe application of adaptive noise cancelers is determining the noisereference signal n′(t) which is correlated to the erratic undesiredportion n(t) of the measured signal S(t) since, as discussed above,unpredictable signal portions are usually quite difficult to isolatefrom the measured signal S(t). In the signal processor of the presentinvention, a noise reference signal n′(t) is determined from twocomposite signals measured simultaneously, or nearly simultaneously, attwo different wavelengths, λa and λb. The signal processor of thepresent invention can be advantageously used in a monitoring device,such a monitor being well suited for physiological monitoring.

A block diagram of a generic monitor incorporating a signal processor,or reference processor, according to the present invention and anadaptive noise canceler is shown in FIG. 4. Two measured signals,S_(λa)(t) and S_(λb)(t), are acquired by a detector 20. One skilled inthe art will realize that for some physiological measurements, more thanone detector may be advantageous. Each signal is conditioned by a signalconditioner 22a and 22b. Conditioning includes, but is not limited to,such procedures as filtering the signals to remove constant portions andamplifying the signals for each of manipulation. The signals are thenconverted to digital data by an analog-to-digital converter 24a and 24b.The first measured signal S_(λa)(t) comprises a first desired signalportion, labelled herein Y_(αa)(t), and a first undesired signalportion, labelled herein n_(λa)(t). The second measured signal S_(λb)(t)is at least partially correlated to the first measured signal S_(λa)(t)and comprises a second desired signal portion, labelled hereinY_(λb)(t), and a second undesired signal portion, labelled hereinn_(λb)(t). Typically the first and second undesired signal portions,n_(λa)(t) and n_(λb)(t), are uncorrelated and/or erratic with respect tothe desired signal portions Y_(λa)(t) and Y_(λb)(t). The undesiredsignal portions n_(λa)(t) and n_(λb)(t) are often caused by motion of apatient. The signals S_(λa)(t) and S_(λb)(t) are input to a referenceprocessor 26. The reference processor 26 multiplies the second measuredsignal S_(λb)(t) by a factor ω and then subtracts the second measuredsignals S_(λb)(t) from the first measured signal S_(λa)(t). The factor ωis determined to cause the desired signal portions Y_(λa)(t) andY_(λb)(t) to cancel when the two signals S_(λa)(t) and S_(λb)(t) aresubtracted. Thus, the output of the reference processor 26 is a noisereference signal n′(t)=n_(λa)(t)−ωn_(λb)(t) which is correlated to bothof the erratic undesired signal portions n_(λa)(t) and n_(λb)(t). Thenoise reference signal n′(t) is input, along with one of the measuredsignals S_(λa)(t), to an adaptive noise canceler 27 which uses the noisereference signal n′(t) to remove the undesired signal portion n_(λa)(t)or n_(λb)(t) from the measured signal S_(λa)(t). It will be understoodthat S_(λb)(t) could have been input to the adaptive noise canceler 27along with the noise reference signal n′(t) instead of S_(λa)(t). Theoutput of the adaptive noise canceler 27 is a good approximationY′_(λa)(t) to the desired signal Y_(λa)(t). The approximation Y′_(λa)(t)is displayed on the display 28.

An adaptive noise canceler 30, an example of which is shown in blockdiagram in FIG. 5, is employed to remove the erratic, undesired signalportions n_(λa)(t) and n_(λb)(t) from the measured signals S_(λa)(t) andS_(λb)(t). The adaptive noise canceler 30 in FIG. 5 has as one input asample of the noise reference signal n′(t) which is correlated to theundesired signal portions n_(λa)(t) and n_(λb)(t). The noise referencesignal n′(t) is determined from the two measured signals S_(λa)(t) andS_(λb)(t) by the processor 26 of the present invention as describedherein. A second input to the adaptive noise canceler is a sample ofeither the first or second measured signal S_(λa)(t)=Y_(λa)(t)+n_(λa)(t)or S_(λb)(t)=Y_(λb)(t)+n_(λb)(t).

The adaptive noise canceler 30 functions to remove frequencies common toboth the noise reference signal n′(t) and the measured signal S_(λa)(t)or S_(λb)(t). Since the noise reference signal n′(t) is correlated tothe erratic undesired signal portions n_(λa)(t) and n_(λb)(t), the noisereference signal n′(t) is also erratic. The adaptive noise canceler actsin a manner which may be analogized to a dynamic multiple notch filterbased on the spectral distribution of the noise reference signal n′(t).

Referring to FIG. 4a, the transfer function of a multiple notch filteris shown. The notches, or dips in the amplitude of the transferfunction, indicate frequencies which are attenuated or removed when acomposite measured signal passes through the notch filter. The output ofthe notch filter is the composite signal having frequencies at which anotch was present removed. In the analogy to an adaptive noise canceler,the frequencies at which notches are present change continuously basedupon the inputs to the adaptive noise canceler.

The adaptive noise canceler 30 shown in FIG. 5 produces an outputsignal, labelled herein Y′_(λa)(t) or Y′_(λb)(t), which is fed back toan internal processor 32 within the adaptive noise canceler 30. Theinternal processor 32 automatically adjusts its own transfer functionaccording to a predetermined algorithm such that the output of theinternal processor 32, labelled b(t), closely resembles the undesiredsignal portion n_(λa)(t) or n_(λb)(t). The output b(t) of the internalprocessor 32 is subtracted from the measured signal, S_(λa)(t) orS_(λb)(t), yielding a signal Y′_(λa)(t)≈S_(λa)(t)+n_(λb)(t)−b_(λb)(t) orY′_(λb)(t)≈S_(λb)(t)+n_(λb)(t)−b_(λb)(t). The internal processoroptimizes Y′_(λa)or Y′_(λb)(t) such that Y′_(λa)(t) or Y′_(λb)(t) isapproximately equal to the desired signal Y_(λa)(t) or Y_(λb)(t),respectively.

One algorithm which may be used for the adjustment of the transferfunction of the internal processor 32 is a least-squares algorithm, asdescribed in Chapter 6 and Chapter 12 of the book Adaptive SignalProcessing by Bernard Widrow and Samuel Stearns, published by PrenticeHall, copyright 1985. This entire book, including Chapters 6 and 12, ishereby incorporated herein by reference.

Adaptive processors 30 have been successfully applied to a number ofproblems including antenna sidelobe canceling, pattern recognition, theelimination of periodic interference in general, and the elimination ofechoes on long distance telephone transmission lines. However,considerable ingenuity is often required to find a suitable noisereference signal n′(t) for a given application since the random orerratic portions n_(λa)(t) or n_(λb)(t) cannot easily be separated fromthe measured signal S_(λa)(t) or S_(λb)(t). If the actual undesiredsignal portion n_(λa)(t) or n_(λb)(t) were a priori available,techniques such as adaptive noise canceling would not be necessary. Theunique determination of a suitable noise reference signal n′(t) frommeasurements taken by a monitor incorporating a reference processor ofthe present invention is one aspect of the present invention.

Generalized Determination of Noise Reference Signal

An explanation which describes how the noise reference signal n′(t) maybe determined as follows. A first signal is measured at, for example, awavelength λa, by a detector yielding a signal S_(λa)(t).

S_(λa)(t)=Y_(λa)(t)+n_(λa)(t);   (1)

Y_(λa)(t) is the desired signal and n_(λa)(t) is the noise component.

A similar measurement is taken simultaneously, or nearly simultaneously,at a different wavelength, λb, yielding:

S_(λb)(t)=Y_(λb)(t)+n_(λb).   (2)

Note that as long as the measurements, S_(λa)(t) and S_(λb)(t), aretaken substantially simultaneously, the undesired signal components,n_(λa)(t) and n_(λb)(t), will be correlated because any random orerratic functions will affect each measurement in nearly the samefashion.

To obtain the noise reference signal n′(t), the measured signalsS_(λa)(t) and S_(λb)(t) are transformed to eliminate the desired signalcomponents. One way of doing this is to find a proportionality constant,ω₁, between the desired signals Y_(λa)(t) and Y_(λb)(t) such that:

Y_(λa)(t)=ω₁Y_(λb)(t).   (3)

This proportionality relationship can be satisfied in many measurements,including but not limited to absorption measurements and physiologicalmeasurements. Additionally, in most measurements, the proportionalityconstant ω₁ can be determined such that:

n_(λa)(t)≠ω₁n_(λb)(t).   (4)

Multiplying equation (2) by ω₁ and then subtracting equation (2) fromequation (1) results in a single equation wherein the desired signalterms Y_(λa)(t) and S_(λb)(t) cancel, leaving:

n′(t)=S_(λa)(t)−ω₁S_(λb)(t)=n_(λa)(t)−ω₁n_(λb)(t);   (5)

a non-zero signal which is correlated to each undesired signal portionn_(λa)(t) and n_(λb)(t) and can be used as the noise reference signaln′(t) in an adaptive noise canceler.

Example of Determination of Noise Reference Signal in an AbsorptiveSystem

Adaptive noise canceling is particularly useful in a large number ofmeasurements generally described as absorption measurements. An exampleof an absorption type monitor which can advantageously employ adaptivenoise canceling based upon a noise reference signal n′(t) determined bya processor of the present invention is one which determines theconcentration of an energy absorbing constituent within an absorbingmaterial when the material is subject to perturbation. Suchperturbations can be caused by forces about which information isdesired, or alternatively, by random or erratic forces such as amechanical force on the material. Random or erratic interference, suchas motion, generates undesired noise components in the measured signal.These undesired components can be removed by the adaptive noise cancelerif a suitable noise reference signal n′(t) is known.

A schematic N constituent absorbing material comprising a container 42having N different absorbing constituents, labelled A₁, A₂, A₃, . . .A_(N), is shown schematically in FIG. 6a. The constituents A₃ throughA_(N) in FIG. 6a are arranged in a generally orderly, layered fashionwithin the container 42. An example of a particular type of absorptivesystem is one in which light energy passes through the container 42 andis absorbed according to the generalized Beer-Lambert Law of lightabsorption. For light of wavelength λa, this attenuation may beapproximated by:

I=I_(o)e^(−Σ) ^(N) ^(i=0εi,λa) ^(c) ^(pei)   (6)

Initially transforming the signal by taking the natural log of bothsides and manipulating terms, the signal is transformed such that thesignal components are combined by addition rather than multiplication,i.e.:

S_(λa)=ln(I_(o)/I)=Σ^(N) _(i=0)ε_(i,λa)c_(i)x_(i)   (7)

where I_(o) is the incident light energy intensity; I is the transmittedlight energy intensity: ε_(i,λa) is the absorption coefficient of thei^(th) constituent at the wavelength λa; x_(i)(t) is the optical pathlength of i^(th) layer, i.e., the thickness of material of the i^(th)layer through which optical energy passes; and c_(i)(t) is theconcentration of the i^(th) constituent in the volume associated withthe thickness x_(i)(t). The absorption coefficients ε₁ through ε_(N) areknown values which are constant at each wavelength. Most concentrationsc₁(t) through c_(N)(t) are typically unknown, as are most of the opticalpath lengths x_(i)(t) of each layer. The total optical path length isthe sum of each of the individual optical path lengths x_(i)(t) of eachlayer.

When the material is not subject to any forces which cause perturbationin the thicknesses of the layers, the optical path length of each layer,x_(i)(t), is generally constant. This results in generally constantattenuation of the optical energy and thus, a generally constant offsetin the measured signal. Typically, this portion of the signal is oflittle interest since knowledge about a force which perturbs thematerial is usually desired. Any signal portion outside of a knownbandwidth of interest, including the constant undesired signal portionresulting from the generally constant absorption of the constituentswhen not subject to perturbation, should be removed. This is easilyaccomplished by traditional band pass filtering techniques. However,when the material is subject to forces, each layer of constituents maybe affected by the perturbation differently than each other layerx_(i)(t) may result in excursions in the measured signal which representdesired information. Other perturbations of the optical path length ofeach layer x_(i)(t) cause undesired excursions which mask desiredinformation in the measured signal. Undesired signal componentsassociated with undesired excursions must also be removed to obtaindesired information from the measured signal.

The adaptive noise canceler removes from the composite signal, measuredafter being transmitted through or reflected from the absorbingmaterial, the undesired signal components cause by forces which perturbthe material differently from the forces which perturbed the material tocause the desired signal component. For the purposes of illustration, itwill be assumed that the portion of the measured signal which is deemedthe desired signal Y_(λa)(t) is the attenuation term ε₅c₅x₅(t)associated with a constituent of interest, namely A₅, and that the layerof constituent A₅ is affected by perturbations differently than each ofthe layers of other constituents A₁ through A₄ and A₆ through A_(N). Anexample of such a situation is when layer A₅ is subject to forces aboutwhich information is desired and, additionally, the entire material issubject to forces which affect each of the layers. In this case, sincethe total force affecting the layer of constituents A₅ is different thanthe total forces affecting each of the other layers and information isdesired about the forces and resultant perturbation of the layer ofconstituents A₅, attenuation terms due to constituents A₁ through A₄ andA₆ through A_(N) make up the undesired signal n_(λa)(t). Even if theadditional forces which affect the entire material cause the sameperturbation in each layer, including the layer of A₅, the total forceson the layer of constituent A₅ cause it to have different totalperturbation than each of the other layers of constituents A₁ through A₄and A₆ through A_(N).

It is often the case that the total perturbation affecting the layersassociated with the undesired signal components is caused by random orerratic forces. This causes the thickness of layers to changeerratically and the optical path length of each layer, x_(i)(t), tochange erratically, thereby producing a random or erratic undesiredsignal component n_(λa)(t). However, regardless of whether or not theundesired signal portion n_(λa)(t) is erratic, the undesired signalcomponent n_(λa)(t) can be removed via an adaptive noise canceler havingas one input a noise reference signal n′(t) determined by a processor ofthe present invention as long as the perturbation on layers other thanthe layer of constituents A₅ is different than the perturbation on thelayer of constituent A₅. The adaptive noise canceler yields a goodapproximation to the desire signal Y′_(λa)(t). From this approximation,the concentration of the constituent of the interest, c₅(t) can often bedetermined since in some physiological measurements, the thickness ofthe desired signal component, x₅(t) in this example, is known or can bedetermined.

The adaptive noise canceler utilizes a sample of a noise referencesignal n′(t) determined from two substantially simultaneously measuredsignals S_(λa)(t) and S_(λb)(t). S_(λa)(t) is determined as above inequation (7). S_(λb)(t) is determined similarly at a differentwavelength λb. To find the noise reference signal n′(t), attenuatedtransmitted energy is measured at the two different wavelengths λa andλb and transformed via logarithmic conversion. The signals S_(λa)(t) andS_(λb)(t) can then be written (logarithm converted) as: $\begin{matrix}{{S_{\lambda \quad a}\quad (t)} = {{\varepsilon_{5\quad \lambda \quad a}\quad c_{5}\quad x_{5}\quad (t)} + \left\lbrack {{\sum\limits_{i = 1}^{4}\quad {\varepsilon_{i\quad \lambda \quad a}\quad c_{i}\quad x_{i}\quad (t)}} + {\sum\limits_{k = 6}^{N}\quad {\varepsilon_{k\quad \lambda \quad a}\quad c_{k}\quad x_{k}\quad (t)}}} \right\rbrack}} & (8) \\{\quad {= {{\varepsilon_{5\quad \lambda \quad a}\quad c_{5}\quad x_{5}\quad (t)} + {n_{\lambda \quad a}\quad (t)}}}} & (9) \\{{S_{\lambda \quad b}\quad (t)} = {{\varepsilon_{5\quad \lambda \quad b}\quad c_{5}\quad x_{5}\quad (t)} + \left\lbrack {{\sum\limits_{i = 1}^{4}\quad {\varepsilon_{i\quad \lambda \quad b}\quad c_{i}\quad x_{i}\quad (t)}} + {\sum\limits_{k = 6}^{N}\quad {\varepsilon_{k\quad \lambda \quad b}\quad c_{k}\quad x_{k}\quad (t)}}} \right\rbrack}} & (10) \\{\quad {= {{\varepsilon_{5\quad \lambda \quad b}\quad c_{5}\quad x_{5}\quad (t)} + {n_{\lambda b}\quad (t)}}}} & (11)\end{matrix}$

A further transformation of the signals is the proportionalityrelationship defining ω₂, similarly to equation (3), which allowsdetermination of a noise reference signal n′(t), is:

ε_(5,λa)=ω₂ε_(5,λb);   (12)

where

n_(λa)≠ω₂n_(λb.)   (13)

It is often the case that the both equations (12) and (13) can besimultaneously satisfied. Multiplying equation (11) by ω₂ andsubtracting the result from equation (9) yields a non-zero noisereference signal which is a linear sum of undesired signal components.$\begin{matrix}{n^{\prime {(t)}} = {{{S_{\lambda \quad a}\quad (t)} - {\omega_{2}\quad S_{\lambda \quad b}\quad (t)}} = {{n_{\lambda \quad a}\quad (t)} - {\omega_{2}\quad n_{\lambda \quad b}\quad {(t).}}}}} & (14) \\\begin{matrix}{\quad {= \quad {{\sum\limits_{i = 1}^{4}\quad {\varepsilon_{i\quad \lambda \quad a}\quad c_{i}\quad x_{i}\quad (t)}} + {\sum\limits_{k = 6}^{N}\quad {\varepsilon_{k\quad \lambda \quad a}\quad c_{k}\quad x_{k}\quad (t)}} - {\sum\limits_{i = 1}^{4}\quad {\omega_{2}\quad \varepsilon_{i\quad \lambda \quad b}\quad c_{i}\quad x_{i}\quad (t)}} -}}} \\{\quad {\sum\limits_{k = 6}^{N}\quad {\omega_{2}\quad \varepsilon_{k\quad \lambda \quad b}\quad c_{k}\quad x_{k}\quad (t)}}}\end{matrix} & (15) \\{\quad {= {{\sum\limits_{i = 1}^{4}\quad {c_{i}\quad x_{i}\quad {(t)\left\lbrack {\varepsilon_{i\quad \lambda \quad a} - {\omega_{2}\quad \varepsilon_{i\quad \lambda \quad b}}} \right\rbrack}}} + {\sum\limits_{k = 6}^{N}\quad {c_{k}\quad x_{k}\quad {(t)\left\lbrack {\varepsilon_{k\quad \lambda \quad a} - {\omega_{2}\quad \varepsilon_{k\quad \lambda \quad b}}} \right\rbrack}}}}}} & (16)\end{matrix}$

A sample of this noise reference signal n′(t), and a sample of eithermeasured signal S_(λa)(t) or S_(λb)(t), are input to an adaptive noisecanceler, one model of which is shown in FIG. 5 and a preferred model ofwhich is discussed herein under the heading PREFERRED ADAPTIVE NOISECANCELER USING A JOINT PROCESS ESTIMATOR IMPLEMENTATION. The adaptivenoise canceler removes the undesired portion of the measured signaln_(λa)(t) or n_(λb)(t), yielding a good approximation to the desiredportion of signal Y′_(λa)(t)≈ε_(5,λa)c₅x₅(t). The concentration c₅(t)may then be determined from the approximation to the desired signalY′_(λa)(t) (t) or Y′_(λb)(t) according to:

c₅(t)≈Y′_(λa)(t)/ε_(5,λa)x₅(t)≈Y′_(λb)(t)/ε_(5,λb)x₅(t).   (17)

As discussed previously, the absorption coefficients are constant ateach wavelength λa and λb and the thickness of the desired signalcomponent, x₅(t) in this example, is often known or can be determined asa function of time, thereby allowing calculation of the concentrationc₅(t) of constituent A₅.

Determination of Concentration or Saturation in a Volume Containing MoreThan One Constituent

Referring to FIG. 6b, another material having N different constituentsarranged in layers is shown. In this material, two constituents A₅ andA₆ are found within one layer having thickness x_(5,6)(t)=x₅(t)+x₆(t),located generally randomly within the layer. This is analogous tocombining the layers of constituents A₅ and A₆ in FIG. 6a. A combinationof layers, such as the combination of layers of constituents A₅ and A₆,is feasible when the two layers are under the same total forces whichresult in the same perturbation of the optical path lengths x₅(t) andx₆(t) of the layers.

Often it is desirable to find the concentration or the saturation, i.e.,a percent concentration, of one constituent within a given thicknesswhich contains more than one constituent and is subject to uniqueforces. A determination of the concentration or the saturation of aconstituent within a given volume may be made with any number ofconstituents in the volume subject to the same total forces andtherefore under the same perturbation. To determine the saturation ofone constituent in a volume comprising many constituents, as manymeasured signals as there are constituents which absorb incident lightenergy are necessary. It will be understood that constituents which donot absorb light energy are not consequential in the determination ofsaturation. To determine the concentration, as many signals as there areconstituents which absorb incident light energy are necessary as well asinformation about the sum of concentrations.

It is often the case that a thickness under unique motion contains onlytwo constituents. For example, it may be desirable to know theconcentration or saturation of A₅ within a given volume which containsA₅ and A₆. In this case, the desired signals Y_(λa)(t) and Y_(λb)(t)comprise terms related to both A₅ and A₆ so that a determination of theconcentration or saturation of A₅ or A₆ in the volume may be made. Adetermination of saturation is discussed herein. It will be understoodthat the concentration of A₅ in volume containing both A₅ and A₆ couldalso be determined if it is known that A₅+A₆=1, i.e., that there are noconstituents in the volume which do not absorb incident light energy atthe particular measurement wavelengths chosen. The measured signalsS_(λa)(t) and S_(λb)(t) can be written (logarithm converted) as:

S_(λa)(t)=ε_(5,λa)c₅x_(5,6)(t)+ε_(6,λa)c₆x_(5,6)(t)+n_(λa)(t)   (18)

 =Y_(λa)(t)+n_(λa)(t);   (19)

S_(λb)(t)=ε_(5,λb)c₅x_(5,6)(t)+ε_(6,λb)c₆x_(5,6)(t)+n_(λb)(t)   (20)

 =Y_(λb)(t)+n_(λb)(t).   (21)

Any signal portions outside of a known bandwidth of interest, includingthe constant undesired signal portion resulting from the generallyconstant absorption of the constituents when not under perturbation,should be removed to determine an approximation to the desired signal.This is easily accomplished by traditional band pass filteringtechniques. As in the previous example, it is often the case that thetotal perturbation affecting the layers associated with the undesiredsignal components is caused by random or erratic forces, causing thethickness of each layer, or the optical path length of each layer,x_(i)(t), to change erratically, producing a random or erratic undesiredsignal component n_(λa)(t). Regardless of whether or not the undesiredsignal portion n_(λa)(t) is erratic, the undesired signal componentn_(λa)(t) can be removed via an adaptive noise canceler having as oneinput a noise reference signal n′(t) determined by a processor of thepresent invention as long as the perturbation in layers other than thelayer of constituents A₅ and A₆ is different than the perturbation inthe layer of constituents A₅ and A₆. The erratic undesired signalcomponents n_(λa)(t) and n_(λb)(t) may advantageously be removed fromequations (18) and (20), or alternatively equations (19) and (21), by anadaptive noise canceler. The adaptive noise canceler, again, requires asample of a noise reference signal n′(t).

Determination of Noise Reference Signal for Saturation Measurement

Two methods which may be used by a processor of the present invention todetermine the noise reference signal n′(t) are a ratiometric method anda constant saturation method. The preferred embodiment of aphysiological monitor incorporating a processor of the present inventionutilizes the ratiometric method wherein the two wavelengths λa and λb,at which the signals S_(λa)(t) and S_(λb)(t) are measured, arespecifically chosen such that a relationship between the absorptioncoefficients ε_(5,λa), ε_(5,λb), ε_(6,λa) and ε_(6,λb) exists, i.e.:

ε_(5,λa)/ε_(6,λa)=ε_(5,λb)/ε_(6,λb)   (22)

The measured signals S_(λa)(t) and S_(λb)(t) can be factored and writtenas:

S_(λa)(t)=ε_(6,λa)[(ε_(5,λa)/ε_(6,λa))c₅x(t)+c₆x(t)]+n_(λa)(t)   (23)

S_(λb)(t)=ε_(6,λb)[(ε_(5,λb)/ε_(6,λb))c₅x(t)+c₆x(t)]+n_(λb)(t).   (24)

The wavelengths λa and λb, chosen to satisfy equation (22), cause theterms within the square brackets to be equal, thereby causing thedesired signal portions Y′_(λa)(t) and Y′_(λb)(t) to be linearlydependent. Then, a proportionality constant ω_(r3) which causes thedesired signal portions Y′_(λa)(t) and Y′_(λb)(t) to be equal and allowsdetermination of a non-zero noise reference signal n′(t) is:

ε_(6,λa)=ω_(r3)ε_(6,λb);   (25)

where

n_(λa)≠ω_(r3)n_(λb).   (b 26)

It is often the case that both equations (25) and (26) can besimultaneously satisfied. Additionally, since absorption coefficients ofeach constituent are constant with respect to wavelength, theproportionality constant ω_(r3) can be easily determined. Furthermore,absorption coefficients of other constituents A₁ through A₄ and A₇through A_(N) are generally unequal to the absorption coefficients of A₅and A₆. Thus, the undesired noise components n_(λa) and n_(λb) aregenerally not made linearly dependent by the relationships of equations(22) and (25).

Multiplying equation (24) by ω_(r3) and subtracting the resultingequation from equation (23), a non-zero noise reference signal isdetermined by:

 n′(t)=S_(λa)(t)−ω_(r3)S_(λb)(t)=n_(λa)(t)−ω_(r3)n_(λb)(t).   (27)

An alternative method for determining the noise reference signal fromthe measured signals S_(λa)(t) and S_(λb)(t) using a processor of thepresent invention is the constant saturation approach. In this approach,it is assumed that the saturation of A₅ in the volume containing A₅ andA₆ remains relatively constant, i.e.: $\begin{matrix}{{{Saturation}\quad \left( {A_{5}\quad (t)} \right)} = {c_{5}\quad (t){\text{/}\left\lbrack {{c_{5}\quad (t)} + {c_{6}\quad (t)}} \right\rbrack}}} & (28) \\{\quad {= \left\{ {1 + \left\lbrack {c_{6}\quad (t)\text{/}c_{5}\quad (t)} \right\rbrack} \right\}^{- 1}}} & (29)\end{matrix}$

is substantially constant over many samples of the measured signalsS_(λa) and S_(λb). This assumption is accurate over many samples sincesaturation generally changes relatively slowly in physiological systems.

The constant saturation assumption is equivalent to assuming that:

c₅(t)/c₆(t)=constant   (30)

since the only other term in equation (29) is a constant, namely thenumeral 1.

Using this assumption, the proportionality constant ω_(s3)(t) whichallows determination of the noise reference signal n′(t) is:$\begin{matrix}{{\omega_{s3}\quad (t)} = \frac{{\varepsilon_{5\quad \lambda \quad a}\quad c_{5}\quad x_{5,6}\quad (t)} + {\varepsilon_{6\quad \lambda \quad a}\quad c_{6}\quad x_{5,6}\quad (t)}}{{\varepsilon_{5\quad \lambda \quad b}\quad c_{5}\quad x_{5,6}\quad (t)} + {\varepsilon_{6\quad \lambda \quad b}\quad c_{6}\quad x_{5,6}\quad (t)}}} & (31) \\{\quad {= {Y_{\lambda \quad a}\quad (t)\text{/}Y_{\lambda \quad b}\quad (t)}}} & (32) \\{\quad {= \frac{{\varepsilon_{5\quad \lambda \quad a}\quad c_{5}} + {\varepsilon_{6\quad \lambda \quad a}\quad c_{6}}}{{\varepsilon_{5\quad \lambda \quad b}\quad c_{5}} + {\varepsilon_{6\quad \lambda \quad b}\quad c_{6}}}}} & (33) \\{\quad {= \frac{{\varepsilon_{5\quad \lambda \quad a}\quad \left( \frac{c_{5}\quad (t)}{c_{6}\quad (t)} \right)} + \varepsilon_{6\quad \lambda \quad a}}{{\varepsilon_{5\quad \lambda \quad b}\quad \left( \frac{c_{5}\quad (t)}{c_{6}\quad (t)} \right)} + \varepsilon_{6\quad \lambda \quad b}}}} & (34) \\{\quad {{\approx {Y_{\lambda \quad a}^{\prime}\quad (t)\text{/}Y_{\lambda \quad b}^{\prime}\quad (t)}} = {{constant}\quad {where}}}} & (35) \\{\quad {{n_{\lambda \quad a}\quad (t)} \neq {\omega_{s3}\quad (t)\quad n_{\lambda \quad b}\quad {(t).}}}} & (36)\end{matrix}$

It is often the case that both equations (35) and (36) can besimultaneously satisfied to determine the proportionality constantω_(s3)(t). Additionally, the absorption coefficients at each wavelengthε_(5,λa), ε_(6,λa), ε_(5,λb), and ε_(6λb) are constant and the centralassumption of the constant saturation method is that c₅(t)/c₆(t) isconstant over many sample periods. Thus, a new proportionality constantω_(a3)(t) may be determined every few samples from new approximations tothe desired signal as output from the adaptive noise canceler. Thus, theapproximations to the desired signals Y′_(λa)(t) and Y′_(λb)(t), foundby the adaptive noise canceler for substantially immediately precedingset of samples of the measured signals S_(λa)(t) and S_(λb)(t) are usedin a processor of the present invention for calculating theproportionality constant, ω_(s3)(t), for the next set of samples of themeasured signals S_(λa)(t) and S_(λb)(t).

Multiplying equation (20) by ω_(s3)(t) and subtracting the resultingequation from equation (18) yields a non-zero noise reference signal:

n′(t)=S_(λa)(t)−ω_(s3)(t)S_(λb)(t)=n_(λa)(t)−ω_(s3)(t)n_(λb)(t).   (37)

It will be understood that equation (21) could be multiplied byω_(s3)(t) and the resulting equation could be subtracted from equation(19) to yield the same noise reference signal n′(t) as given in equation(37).

When using the constant saturation method, it is necessary for thepatient to remain motionless for a short period of time such that anaccurate initial saturation value can be determined by known methodsother than adaptive noise canceling on which all other calculations willbe based. With no erratic, motion-induced undesired signal portions, aphysiological monitor can very quickly produce an initial value of thesaturation of A₅ in the volume containing A₅ and A₆. An example of asaturation calculation is given in the article “SPECTROPHOTOMETRICDETERMINATION OF OXYGEN SATURATION OF BLOOD INDEPENDENT OF THE PRESENTOF INDOCYANINE GREEN” by G. A. Mook, et al., wherein determination ofoxygen saturation in arterial blood is discussed. Another articlediscussing the calculation of oxygen saturation is “PULSE OXIMETRY:PHYSICAL PRINCIPLES, TECHNICAL REALIZATION AND PRESENT LIMITATIONS” byMichael R. Neuman. Then, with values for Y′_(λa)(t) and Y′_(λb)(t)determined, an adaptive noise canceler may be utilized with a noisereference signal n′(t) determined by the constant saturation method.

Preferred Adaptive Noise Canceler Using a Joint Process EstimatorImplementation

Once the noise reference signal n′(t) is determined by the processor ofthe present invention using either the above described ratiometric orconstant saturation methods, the adaptive noise canceler can beimplemented in either hardware or software.

The least mean squares (LMS) implementation of the internal processor 32described above in conjunction with the adaptive noise canceler of FIG.5 is relatively easy to implement, but lacks the speed of adaptationdesirable for most physiological monitoring applications of the presentinvention. Thus, a faster approach for adaptive noise canceling, calleda least-squares lattice joint process estimator model, is preferablyused. A joint process estimator 60 is shown diagrammatically in FIG. 7and is described in detail in Chapter 9 of Adaptive Filter Theory bySimon Haykin, published by Prentice-Hall, copyright 1986. This entirebook, including Chapter 9, is hereby incorporated herein by reference.The function of the joint process estimator is to remove the undesiredsignal portions n_(λa)(t) or n_(λb)(t) from the measured signalsS_(λa)(t) or S_(λb)(t), yielding a signal Y′_(λa)(t) or Y′_(λb)(t) whichis a good approximation to the desired signal Y_(λa)(t) or Y_(λb)(t).Thus, the joint process estimator estimates the value of the desiredsignal Y_(λa)(t) or Y_(λb)(t). The inputs to the joint process estimator60 are the noise reference signal n′(t) and the composite measuredsignal S_(λa)(t) or S_(λb)(t). The output is a good approximation to thesignal S_(λa)(t) or S_(λb)(t) with the noise removed, i.e. a goodapproximation to Y_(λa)(t) or Y_(λb)(t).

The joint process estimator 60 utilizes, in conjunction, a least squarelattice predictor 70 and a regression filter 80. The noise referencesignal n′(t) is input to the least square lattice predictor 70 while themeasured signal S_(λa)(t) or S_(λb)(t) is input to the regression filter80. For simplicity in the following description, S_(λa)(t) will be themeasured signal from which the desired portion Y_(λa)(t) will beestimated by the joint process estimator 60. However, it will be notedthat S_(λb)(t) could equally well be input to the regression filter 80and the desired portion Y_(λb)(t) of this signal could equally well beestimated.

The joint process estimator 60 removes all frequencies that are presentin both the noise reference signal n′(t) and the measured signalS_(λa)(t). The undesired signal portion n_(λa)(t) usually comprisesfrequencies unrelated to those of the desired signal portion Y_(λa)(t).It is highly improbable that the undesired signal portion n_(λa)(t)would be of exactly the same spectral content as the desired signalportion Y_(λa)(t). However, in the unlikely event that the spectralcontent of S_(λa)(t) and n′(t) are similar, this approach will not yieldaccurate results. Functionally, the joint process estimator 60 comparesinput signal n′(t), which is correlated to the undesired signal portionn_(λa)(t), and input signal S_(λa)(t) and removes all frequencies whichare identical. Thus, the joint process estimator 60 acts as a dynamicmultiple notch filter to remove those frequencies in the undesiredsignal component n_(λa)(t) as they change erratically with the motion ofthe patient. This yields a signal having substantially the same spectralcontent as the desired signal Y_(λa)(t). The output of the joint processestimator 60 has substantially the same spectral content and amplitudeas the desired signal Y_(λa)(t). Thus, the output Y′_(λa)(t) of thejoint process estimator 60 is a very good approximation to the desiredsignal Y_(λa)(t).

The joint process estimator 60 can be divided into stages, beginningwith a zero-stage and terminating in an m^(th)-stage, as shown in FIG.7. Each stage, except for the zero-stage, is identical to every otherstage. The zero-stage is an input stage for the joint process estimator60. The first stage through the m^(th)-stage work on the signal producedin the immediately previous stage, i.e., the (m−1)^(th)-stage, such thata good approximation to the desired signal Y′_(λa)(t) is produced asoutput from the m^(th)-stage.

The least-squares lattice predictor 70 comprises registers 90 and 92,summing elements 100 and 102, and delay elements 110. The registers 90and 92 contain multiplicative values of a forward reflection coefficientΓ_(b,m)(t) and a backward reflection coefficient Γ_(b,m)(t) whichmultiply the noise reference signal n′(t) and signals derived from thenoise reference signal n′(t). Each stage of the least-squares latticepredictor outputs a forward prediction error f_(m)(t) and a backwardprediction error b_(m)(t). The subscript m is indicative of the stage.

For each set of samples, i.e. one sample of the noise reference signaln′(t) derived substantially simultaneously with one sample of themeasured signal S_(λa)(t), the sample of the nose reference signal n′(t)is input to the lead-squares lattice predictor 70. The zero-stageforward predictor error f₀(t) and the zero-stage backward predictionerror b₀(t) are set equal to the noise reference signal n′(t). Thebackward prediction error b₀(t) is delayed by one sample period by thedelay element 110 in the first stage of the least-squares latticepredictor 70. Thus, the immediately previous value of the noisereference signal n′(t) is used in calculations involving the first-stagedelay element 110. The zero-stage forward prediction error is added tothe negative of the delayed zero-stage backward prediction error b₀(t−1)multiplied by the forward reflection coefficient value Γ_(f,1)(t)register 90 value, to produce a first-stage forward prediction errorf₁(t). Additionally, the zero-stage forward prediction error f₀(t) ismultiplied by the backward reflection coefficient value Γ_(b,1 (t))register 92 value and added to the delayed zero-stage backwardprediction error b₀(t−1) to produce a first-stage backward predictionerror b₁(t). In each subsequent stage, m, of the least square latticepredictor 70, the previous forward and backward prediction error values,f_(m-1)(t) and b_(m-1)(t−1), the backward prediction error being delayedby one sample period, are used to produce values of the forward andbackward prediction errors for the present stage, f_(m)(t) and b_(m)(t).

The backward prediction error b_(m)(t) is fed to the concurrent stage,m, of the regression filter 80. There it is input to a register 96,which contains a multiplicative regression coefficient valueκ_(m,λa)(t). For example, in the zero-stage of the regression filter 80,the zero-stage backward prediction error b₀(t) is multiplied by thezero-stage regression coefficient κ_(0,λa)(t) register 96 value andsubtracted from the measured value of the signal S_(λa)(t) at a summingelement 106 to produce a first stage estimation error signale_(1,λa)(t). The first-stage estimation error signal e_(1,λa)(t) is afirst approximation to the desired signal. This first-stage estimationerror signal e_(1,λa)(t) is input to the first-stage of the regressionfilter 80. The first-stage backward prediction error b₁(t), multipliedby the first-stage regression coefficient κ_(1,λa)(t) register 96 valueis subtracted from the first-stage estimation error signal e_(1,λa)(t)to produce the second-stage estimation error e_(2,λa)(t). Thesecond-stage estimation error signal e_(2,λa)(t) is a second, somewhatbetter approximation to the desired signal Y_(λa)(t).

The same processes are repeated in the least-squares lattice predictor70 and the regression filter 80 for each stage until a goodapproximation to the desired signal Y′_(λa)(t)=e_(m,λa)(t) isdetermined. Each of the signals discussed above, including the forwardprediction error f_(m)(t), the backward prediction error b_(m)(t), theestimation error signal e_(m,λa)(t), is necessary to calculate theforward reflection coefficient Γ_(f,m)(t), the backward reflectioncoefficient Γ_(b,m)(t), and the regression coefficient κ_(m,λa)(t)register 90, 92, and 96 values in each stage, m. In addition to theforward prediction error f_(m)(t), the backward prediction errorb_(m)(t), and the estimation error e_(m,λa)(t) signals, a number ofintermediate variables, not shown in FIG. 7 but based on the valueslabelled in FIG. 7, are required to calculate the forward reflectioncoefficient Γ_(fm,)(t), the backward reflection coefficient Γ_(b,m)(t),and the regression coefficient κ_(m,λa)(t) register 90, 92, and 96values.

Intermediate variables include a weighted sum of the forward predictionerror squares F_(m)(t), a weighted sum of the backward prediction errorsquares β_(m)(t), a scaler parameter Δ_(m)(t), a conversion factorγ_(m)(t), and another scaler parameter ρ_(m,λa)(t). The weighted sum ofthe forward prediction errors F_(m)(t) is defined as: $\begin{matrix}{{{F_{m}\quad (t)} = {\sum\limits_{i = 1}^{t}\quad {\lambda^{t - i}{{f_{m}\quad (i)}}^{2}}}};} & (38)\end{matrix}$

where λ without a wavelength identifier, a or b, is a constantmultiplicative value unrelated to wavelength and is typically less thanor equal to one, i.e., λ≦1. The weighted sum of the backward predictionerrors β_(m)(t) is defined as: $\begin{matrix}{{\beta_{m}\quad (t)} = {\sum\limits_{i = 1}^{t}\quad {\lambda^{t - i}{{b_{m}\quad (i)}}^{2}}}} & (39)\end{matrix}$

where, again, λ without a wavelength identifier, a or b, is a constantmultiplicative value unrelated to wavelength and is typically less thanor equal to one, i.e., λ≦1. These weighted sum intermediate errorsignals can be manipulated such that they are more easily solved for, asdescribed in Chapter 9, §9.3, and defined hereinafter in equations (53)and (54).

Description of the Joint Process Estimator

The operation of the joint process estimator 60 is as follows. When thejoint process estimator 60 is turned on, the initial values ofintermediate variable and signal including the parameter Δ_(m-1)(t), theweighted sum of the forward prediction error signals F_(m-1)(t), theweighted sum of the backward prediction error signals β_(m-1)(t), theparameter ρ_(m,λa)(t), and the zero-stage estimation error e_(0,λa)(t)are initialized, some to zero and some to a small positive number δ:

Δ_(m-1)(0)=0;   (40)

F_(m-1)(0)=δ;   (41)

β_(m-1)(0)=δ;   (42)

ρ_(m,λa)(0)=0;   (43)

e_(0,λa)(t)=S_(λa)(t) for t≧0.   (44)

After initialization, a simultaneous sample of the measured signalS_(λa)(t) and the noise reference signal n′(t) are input to the jointprocess estimator 60, as shown in FIG. 7. The forward and backwardprediction error signals f₀t and b₀t, and intermediate variablesincluding the weighted sums of the forward and backward error signalsƒ₀t and β₀t, and the conversion factor τ_(O)(t) are calculated for thezero-stage according to:

f₀(t)=b₀(t)=n′(t)   (45)

F₀(t)=β₀(t)=λF₀(t−1)+|n′(t)|²   (46)

γ₀(t−1)=1   (47)

where, again, λ without a wavelength identifier, a or b, is a constantmultiplicative value unrelated to wavelength.

Forward reflection coefficient Γ_(f,m)(t), backward reflectioncoefficient Γ_(b,m)(t), and regression coefficient κ_(m,λa)(t) register90, 92 and 96 values in each stage thereafter are set according to theoutput of the previous stage. The forward reflection coefficientΓ_(f,1)(t), backward reflection coefficient Γ_(b,1)(t), and regressioncoefficient κ_(1,λa)(t) register 90, 92 and 96 values in the first stageare thus set according to algorithm using values in the zero-stage ofthe joint process estimator 60. In each stage, m≧1, intermediate valuesand register values including the parameter Δ_(m-1)(t); the forwardreflection coefficient Γ_(f,m)(t) register 90 value; the backwardreflection coefficient Γ_(b,m)(t) register 92 value; the forward andbackward error signals f_(m)(t) and b_(m)(t); the weighted sum ofsquared forward prediction errors F_(f,m)(t), as manipulated in § 9.3 ofthe Haykin book; the weighted sum of squared backward prediction errorsβ_(b,m)(t), as manipulated in § 9.3 of the Haykin book; the conversionfactor γ_(m)(t); the parameter ρ_(m,λa)(t); the regression coefficientκ_(m,λa)(t) register 96 value; and the estimation error e_(m+1,λa)(t)value are set according to:

Δ_(m-1)(t)=λΔ_(m-1)(t−1)+{b_(m-1)(t−1)f*_(m-1)(t−1)}  (48)

Γ_(f,m)(t)=−{Δ_(m-1)(t)/β_(m-1)(t−1}  (49)

Γ_(b,m)(t)=−{Δ*_(m-1)(t)/F_(m-1)(t−1)}  (50)

f_(m)(t)=f_(m-1)(t)+Γ*_(f,m)(t)b_(m-1)(t−1)   (51)

b_(m)(t)=b_(m-1)(t−1)+Γ*_(b,m)(t)f_(m-1)(t)   (52)

F_(m)(t)=F_(m-1)(t)−{|Δ_(m-1)(t)|²/β_(m-1)(t−1)}  (53)

β_(m)(t)=β_(m-1)(t−1)−{|Δ_(m-1)(t)|²/F_(m-1)(t)}  (54)

γ_(m)(t−1)=γ_(m-1)(t−1)−{|b_(m-1)(t−1)(|²/β_(m-1)(t−1)}  (55)

ρ_(m,λa)(t)=λρ_(m,λa)(t−1)+{b_(m)(t)e*_(m,λa)(t)/γ_(m)(t)}  (56)

κ_(m,λa)(t)={ρ_(m,λa)(t)/β_(m)(t)}  (57)

e_(m+1,λa)(t)=e_(n,λa)(t)−κ*_(m)(t)b_(m)(t)   (58)

where a (*) denotes a complex conjugate.

These equations cause the error signals f_(m)(t), b_(m)(t), e_(m,λa)(t)to be squared or to be multiplied by one another, in effect squaring theerrors, and creating new intermediate error values, such as Δ_(m-1)(t).The error signals and the intermediate error values are recursively tiedtogether, as shown in the above equations (48) through (58). Theyinteract to minimize the error signals in the next stage.

After a good approximation to the desired signal Y′_(λa)(t) has beendetermined by the joint process estimator 60, a next set of samples,including a sample of the measured signal S_(λa)(t) and a sample of thenoise reference signal n′(t), are input to the joint process estimator60. The re-initialization process does not re-occur, such that theforward and backward reflection coefficient Γ_(r,m)(t) and Γ_(b,m)(t)register 90, 92 values and the regression coefficient κ_(m,λa)(t)register 96 value reflect the multiplicative values required to estimatethe desired portion Y_(λa)(t) of the sample of S_(λa)(t) inputpreviously. Thus, information from previous samples is used to estimatethe desired signal portion of a present set of samples in each stage.

Flowchart of Joint Process Estimator

In a signal processor, such as a physiological monitor, incorporating areference processor of the present invention to determine a noisereference signal n′(t) for input to an adaptive noise canceler, a jointprocess estimator 60 type adaptive noise canceler is generallyimplemented via a software program having an interactive loop. Oneiteration of the loop is analogous to a single stage of the jointprocess estimator as shown in FIG. 7. Thus, if a loop is iterated mtimes, it is equivalent to an m stage joint process estimator 60.

A flow chart of a subroutine to estimate the desired signal portionY_(λa)(t) of a sample of a measured signal, S_(λa)(t) is shown in FIG.8. The flow chart describes how the action of a reference processor fordetermining the noise reference signal and the joint process estimator60 would be implemented in software.

A one-time only initialization is performed when the physiologicalmonitor is turned on, as indicated by an “INITIALIZE NOISE CANCELER” box120. The initialization sets all registers 90, 92, and 96 and delayelement variables 110 to the values described above in equations (40)through (44).

Next, a set of simultaneous samples of the measured signals S_(λa)(t)and S_(λb)(t) is input to the subroutine represented by the flowchart inFIG. 8. Then a time update of each of the delay element program variableoccurs, as indicated in a “TIME UPDATE OF [Z⁻¹] ELEMENTS” box 130,wherein the value stored in each of the delay element variables 110 isset to the value at the input of the delay element variables 110. Thus,the zero-stage backward prediction error b₀(t) is stored in thefirst-stage delay element variable, the first-stage backward predictionerror b₁(t) is stored in the second-stage delay element variable, and soon.

Then, using the set of measured signal samples S_(λs)(t) and S_(λb)(t),the noise reference signal is calculated according to the ratiometric orthe constant saturation method described above. This is indicated by a“CALCULATE NOISE REFERENCE (n′(t)) FOR TWO MEASURED SIGNAL SAMPLES” box140. The ratiometric method is generally preferred since no assumptionsabout constant saturation values need be made.

A zero-stage order update is performed next as indicated in a“ZERO-STAGE UPDATE” box 150. The zero-stage backward prediction errorb₀(t), and the zero-stage forward prediction error f₀(t) are set equalto the value of the noise reference signal n′(t). Additionally, theweighted sum of the forward prediction errors F_(m)(t) and the weightedsum of backward prediction errors β_(m)(t) are set equal to the valuedefined in equation (46).

Next, a loop counter, m, is initialized as indicated in a “m=0” box 160.A maximum value of m, defining the total number of stages to be used bythe subroutine corresponding to the flowchart in FIG. 8, is alsodefined. Typically, the loop is constructed such that it stops iteratingonce a criterion for convergence upon a best approximation to thedesired signal has been met by the joint process estimator 60.Additionally, a maximum number of loop iterations may be chosen at whichthe loop stops iteration. In a preferred embodiment of a physiologicalmonitor of the present invention, a maximum number of iterations, m=60to m=80, is advantageously chosen.

Within the loop, the forward and backward reflection coefficientΓ_(f,m)(t) and Γ_(b,m)(t) register 90 and 92 values in the least-squareslattice filter are calculated first, as indicated by the “ORDER UPDATEMTH CELL OF LSL-LATTICE” box 170 in FIG. 8. This requires calculation ofintermediate variable and signal values used in determining register 90,92, and 96 values in the present stage, the next stage, and in theregression filter 80.

The calculation of regression filter register 96 value κ_(m,λa)(t) isperformed next, indicated by the “ORDER UPDATE MTH STAGE OF REGRESSIONFILTER(S)” box 180. The two order update boxes 170 and 180 are performedin sequence m times, until m has reached its predetermined maximum (inthe preferred embodiment, n=60 to m=80) or a solution has been convergedupon, as indicated by a YES path from a “DONE” decision box 190. mn acomputer subroutine, convergence is determined by checking if theweighted sums of the forward and backward prediction errors F_(m)(t) andβ_(m)(t) are less than a small positive number. An output is calculatednext, as indicated by a “CALCULATE OUTPUT” box 200. The output is a goodapproximation to the desired signal, as determined by the referenceprocessor and joint process estimator 60 subroutine corresponding to theflow chart of FIG. 8. This is displayed (or used in a calculation inanother subroutine), as indicated by a “TO DISPLAY” box 210.

A new set of samples of the two measured signals S_(λa)(t) and S_(λb)(t)is input to the processor and joint process estimator 60 adaptive noisecanceler subroutine corresponding to the flowchart of FIG. 8 and theprocess reiterates for these samples. Note, however, that theinitialization process does not re-occur. New sets of measured signalsamples S_(λa)(t) an S_(λb)(t) are continuously input to the referenceprocessor and joint process estimator 60 adaptive noise cancelersubroutine. The output forms a chain of samples which is representativeof a continuous wave. This waveform is a good approximation to thedesired signal waveform Y′_(λa)(t) at wavelength λa.

Calculation of Saturation from Adaptive Noise Canceler Output

Physiological monitors typically use the approximation of the desiredsignal Y′_(λa)(t) to calculate another quantity, such as the saturationof one constituent in a volume containing that constituent plus one ormore other constituents. Generally, such calculations requireinformation about a desired signal at two wavelengths. In somemeasurements, this wavelength is λb, the wavelength used in thecalculation of the noise reference signal n′(t). For example, theconstant saturation method of determining the noise reference signalrequires a good approximation of the desired signal portions Y_(λa)(t)and Y_(λb)(t) of both measured signals S_(λa)(t) and S_(λb)(t). Then,the saturation is determined from the approximations to both signals,i.e. Y′_(λa)(t) and Y′_(λb)(t).

In other physiological measurements, information about a signal at athird wavelength is necessary. For example, to find the saturation usingthe ratiometric method, signals S_(λa)(t) and S_(λb)(t) are used to findthe noise reference signal n′(t). But as discussed previously, _(λa) and_(λb) were chosen to satisfy a proportionately relationship like that ofequation (22). This proportionality relationship forces the two desiredsignal portions Y_(λa)(t) and Y_(λb)(t) to be linearly dependent.Generally, linearly dependant mathematical equations cannot be solvedfor the unknowns. Analogously, some desirable information cannot bederived from two linearly dependent signals. Thus, to determine thesaturation using the ratiometric method, a third signal issimultaneously measured at wavelength λc. The wavelength λc is chosensuch that the desired portion Y_(λc)(t) of the measured signal S_(λc)(t)is not linearly dependent with the desired portions Y_(λa)(t) andY_(λb)(t) of the measured signals S_(λa)(t) and S_(λb)(t). Since allmeasurements are taken substantially simultaneously, the noise referencesignal n′(t) is correlated to the undesired signal portions n_(λa),n_(λb), and n_(λc) of each of the measured signals S_(λa)(t), S_(λb)(t),and S_(λc)(t) can be used to estimate approximations to the desiredsignal portions Y_(λa)(t), Y_(λb)(t), and Y_(λc)(t), for all threemeasured signals S_(λa)(t), S_(λb)(t), S_(λc)(t). Using the ratiometricmethod, estimation of the desired signal portions Y_(λa)(t) andY_(λc)(t) of two measured signals S_(λa)(t) and S_(λc)(t), chosencorrectly, is usually satisfactory to determine most physiological data.

A joint process estimator 60 having two regression filters 80a and 80bis shown in FIG. 9. A first regression filter 80a accepts a measuredsignal S_(λa)(t). A second regression filter 80b accepts a measuredsignal S_(λb)(t) or the ratiometric method is used to determine thenoise reference signal n′(t). The first and second regression filters80a and 80b are independent. The backward prediction error b_(m)(t) isinput to each regression filter 80a and 80b, the input for the secondregression filter 80b bypassing the first regression filter 80a.

The second regression filter 80b comprises registers 98, and summingelements 108 arranged similarly to those in the first regression filter80a. The second regression filter 80b operates via an additionalintermediate variable in conjunction with those defined by equations(48) through (58), i.e.:

ρ_(m,λb)(t)=λρ_(m,λb)(t−1)+{b_(m)(t)e*_(m,λb)(t)/γ_(m)(t)}; or   (59)

ρ_(m,λc)(t)=λρ_(m,λc)(t−1)+{b_(m)(t)e*_(m,λc)(t)/γ_(m)(t)}; and   (60)

ρ_(0,λb)(0)=0; or   (61)

ρ_(0,λc)(0)=0.   (62)

The second regression filter 80b has an error signal value definedsimilar to the first regression filter error signal values,e_(m+1,λa)(t), i.e.:

e_(m+1,λb)(t)=e_(m,λb)(t)−κ*_(m,λb)(t)b_(m)(t); or   (63)

e_(m+,λc)(t)=e_(m,λc)(t)−κ*_(m,λb)(t)b_(m)(t); and   (64)

e_(0,λb)(t)=S_(λb)(t) for t≧0; or   (65)

 e_(0,λc)(t)=S_(λc)(t) for t≧0.   (66)

The second regression filter has a regression coefficient κ_(m,λb)(t)register 98 value defined similarly to the first regression filter errorsignal values, i.e.:

κ_(m,λb)(t)={ρ_(m,λb)(t)/β_(m)(t)}; or   (67)

κ_(m,λc)(t)={ρ_(m,λc)(t)/β_(m)(t)};   (68)

These values are used in conjunction with those intermediate variablevalues, signal values, register and register values defined in equations(40) through (58). These signals are calculated in an order defined byplacing the additional signals immediately adjacent a similar signal forthe wavelength λa.

For the ratiometric method, S_(λc)(t) is input to the second regressionfilter 80b. The output of the second regression filter 80b is then agood approximation to the desired signal Y′_(λc)(t). For the constantsaturation method, S_(λb)(t) is input to the second regression filter80b. The output is then a good approximation to the desired signalY′_(λb)(t).

The addition of the second regression filter 80b does not substantiallychange the computer program subroutine represented by the flowchart ofFIG. 8. Instead of an order update of the m^(th) stage of only oneregression filter, an order update of the m^(th) stage of bothregression filters 80a and 80b is performed. This is characterized bythe plural designation in the “ORDER UPDATE OF m^(th) STAGE OFREGRESSION FILTER(S)” box 180 in FIG. 8. Since the regression filters80a and 80b operate independently, independent calculations can beperformed in the reference processor and joint process estimator 60adaptive noise canceler subroutine modeled by the flowchart of FIG. 8.

Calculation of Saturation

Once good approximations to the desired signals, Y′_(λa)(t) andY′_(λc)(t) for the ratiometric method and Y′_(λa)(t) and Y′_(λb)(t) forthe constant saturation method, have been determined by the jointprocess estimator 60, the saturation of A₅ in a volume containing A₅ andA₆, for example, may be calculated according to various known methods.Mathematically, the approximations to the desired signals can bewritten:

Y′_(λa)(t)≈ε_(5,λa)c₅x_(5,6)(t)+ε_(6,λa)c₆x_(5,6)(t); and   (69)

Y′_(λc)(t)≈ε_(5,λc)c₅x_(5,6)(t)+ε_(6,λc)c₆x_(5,6)(t).   (70)

for the ratiometric method using wavelengths λa and λc. For the constantsaturation method, the approximations to the desired signals can bewritten in terms of λa and λb as:

Y′_(λa)(t)≈ε_(5,λa)c₅x_(5,6)(t)+ε_(6,λa)c₆x_(5,6)(t); and   (71)

Y′_(λb)(t)≈ε_(5,λb)c₅x_(5,6)(t)+ε_(6,λb)c₆x_(5,6)(t).   (72)

This is equivalent to two equations having three unknowns, namely c₅(t),c₆(t) and x_(5,6)(t). In both the ratiometric and the constantsaturation cases, the saturation can be determined by acquiringapproximations to the desired signal portions at two different, yetproximate times t₁ and t₂ over which the saturation of A₅ in the volumecontaining A₅ and A₆ does not change substantially. For example, for thedesired signals estimated by the ratiometric method, at times t₁ and t₂:

Y′_(λa)(t₁)≈ε_(5,λa)c₅x_(5,6)(t₁)+ε_(6,λa)c₆x_(5,6)(t₁)   (73)

Y′_(λc)(t₁)≈ε_(5,λc)c₅x_(5,6)(t₁)+ε_(6,λc)c₆x_(5,6)(t₁)   (74)

Y′_(λa)(t₂)≈ε_(5,λa)c₅x_(5,6)(t₂)+ε_(6,λa)c₆x_(5,6)(t₂)   (75)

Y′_(λc)(t₂)≈ε_(5,λc)c₅x_(5,6)(t₂)+ε_(6,λc)c₆x_(5,6)(t₂)   (76)

Then, difference signals may be determined which relate the signals ofequation (73) through (76), i.e.:

ΔY_(λa)≈Y′_(λa)(t₁)−Y′_(λa)(t₂)=ε_(5,λa)c₅Δx+ε_(6,λa)c₆Δx; and   (77)

ΔY_(λc)≈Y′_(λc)(t₁)−Y′_(λc)(t₂)=ε_(5,λc)c₅Δx+ε_(6,λc)c₆Δx;   (78)

where Δx=x_(5,6)(t₁)−x_(5,6)(t₂) The average saturation at timet=(t₁+t₂)/2 is: $\begin{matrix}{{{Saturation}\quad (t)} = {c_{5}\quad (t){\text{/}\left\lbrack {{c_{5}\quad (t)} + {c_{6}\quad (t)}} \right\rbrack}}} & (79) \\{\quad {= \frac{\varepsilon_{6\quad \lambda \quad a} - {\varepsilon_{6\quad \lambda \quad b}\quad \left( \frac{\Delta \quad Y_{\lambda \quad a}}{\Delta \quad Y_{\lambda \quad b}} \right)}}{\varepsilon_{6\quad \lambda \quad a} - \varepsilon_{5\quad \lambda \quad a} - {\left( {\varepsilon_{6\quad \lambda \quad b} - \varepsilon_{5\quad \lambda \quad b}} \right)\quad \left( \frac{\Delta \quad Y_{\lambda \quad a}}{\Delta \quad Y_{\lambda \quad b}} \right)}}}} & (80)\end{matrix}$

It will be understood that the Δx term drops out from the saturationcalculation because of the division. Thus, knowledge of the thickness ofthe desired constituents is not required to calculate saturation.

Pulse Oximetry Measurements

A specific example of a physiological monitor utilizing a processor ofthe present invention to determine a noise reference signal n′(t) forinput to an adaptive noise canceler that removes erratic motion-inducedundesired signal portions is a pulse oximeter. A pulse oximetertypically causes energy to propagate through a medium where blood flowsclose to the surface for example, an ear lobe, or a digit such as afinger, or a forehead. An attenuated signal is measured afterpropagation through or reflection from the medium. The pulse oximeterestimates the saturation of oxygenated blood available to the body foruse.

Freshly oxygenated blood is pumped at high pressure from the heart intothe arteries for use by the body. The volume of blood in the arteriesvaries with the heartbeat, giving rise to a variation in absorption ofenergy at the rate of the heartbeat, or the pulse.

Oxygen depleted, or deoxygenated, blood is returned to the heart by theveins along with unused oxygenated blood. The volume of blood in theveins varies with the rate of breathing, which is typically much slowerthan the heartbeat. Thus, when there is no motion induced variation inthe thickness of the veins, venous blood causes a low frequencyvariation in absorption of energy. When there is motion inducedvariation in the thickness of veins, the low frequency variation inabsorption is coupled with the erratic variation in absorption due tomotion artifact.

In absorption measurements using the transmission of energy through amedium, two light emitting diodes (LED's) are positioned on one side ofa portion of the body where blood flows close to the surface, such as afinger, and a photodetector is positioned on the opposite side of thefinger. Typically, in pulse oximetry measurements, one LED emits avisible wavelength, preferably red, and the other LED emits an infraredwavelength. However, one skilled in the art will realize that otherwavelength combinations could be used.

The finger comprises skin, tissue, muscle, both arterial blood andvenous blood, fat, etc., each of which absorbs light energy differentlydue to different absorption coefficients, different concentrations, anddifferent thicknesses. When the patient is not moving, absorption issubstantially constant except for the flow of blood. This constantattenuation can be determined and subtracted from the signal viatraditional filtering techniques. When the patient moves, the absorptionbecomes erratic. Erratic motion induced noise typically cannot bepredetermined and subtracted from the measured signal via traditionalfiltering techniques. Thus, determining the saturation of oxygenatedarterial blood becomes more difficult.

A schematic of a physiological monitor for pulse oximetry is shown inFIG. 10. Two LED's 300 and 302, one LED 300 emitting red wavelengths andanother LED 302 emitting infrared wavelengths, are placed adjacent afinger 310. A photodetector 320, which produces an electrical signalcorresponding to the attenuated visible and infrared light energysignals is located opposite the LED's 300 and 302. The photodetector 320is connected to a single channel of common processing circuitryincluding an amplifier 330 which is in turn connected to a band passfilter 340. The band pass filter 340 passes signal into a synchronizeddemodulator 350 which has a plurality of output channels. One outputchannel is for signals corresponding to visible wavelengths and anotheroutput channel is for signals corresponding to infrared wavelengths.

The output channels of the synchronized demodulator for signalscorresponding to both the visible and infrared wavelengths are eachconnected to separate paths, each path comprising further processingcircuitry. Each path includes a DC offset removal element 360 and 362,such as a differential amplifier, a programmable gain amplifier 370 and372 and a low pass filter 380 and 382. The output of each low passfilter 380 and 382 is amplified in a second programmable gain amplifier390 and 392 and then input to a multiplexer 400.

The multiplexer 400 is connected to an analog-to-digital converter 410which is in turn connected to a microprocessor 420. Control linesbetween the microprocessor 420 and the multiplexer 400, themicroprocessor 420 and the analog-to-digital converter 410, and themicroprocessor 420 and each programmable gain amplifier 370, 372, 390,and 392 are formed. The microprocessor 420 has additional control lines,one of which leads to a display 430 and the other of which leads to anLED driver 440 situated in a feedback loop with the two LED's 300 and302.

The LED's 300 and 302 each emits energy which is absorbed by the finger310 and received by the photodetector 320. The photodetector 320produces an electrical signal which corresponds to the intensity of thelight energy striking the photodetector 320 surface. The amplifier 330amplifies this electrical signal for ease of processing. The band passfilter 340 then removes unwanted high and low frequencies. Thesynchronized demodulator 350 separates the electrical signal intoelectrical signals corresponding to the red and infrared light energycomponents. A predetermined reference voltage, V_(ref), is subtracted bythe DC offset removal element 360 and 362 from each of the separatesignals to remove substantially constant absorption which corresponds toabsorption when there is not motion induced undesired signal component.Then the first programmable gain amplifiers 370 and 372 amplify eachsignal for ease of manipulation. The low pass filters 380 and 382integrate each signal to remove unwanted high frequency components andthe second programmable gain amplifiers 390 and 392 amplify each signalfor further ease of processing.

The multiplexer 400 acts as an analog switch between the electricalsignals corresponding to the red and the infrared light energy, allowingfirst a signal corresponding to the red light to enter theanalog-to-digital converter 410 and then a signal corresponding to theinfrared light to enter the analog-to-digital converter 410. Thiseliminates the need for multiple analog-to-digital convertors 410. Theanalog-to-digital convertor 410 inputs the data into the microprocessor420 for calculation of a noise reference signal via the processingtechnique of the noise reference signal via the processing technique ofthe present invention and removal of undesired signal portions via anadaptive noise canceler. The microprocessor 420 centrally controls themultiplexer 400, the analog-to-digital converter 410, and the first andsecond programmable gain amplifiers 370 and 390 for both the red and theinfrared channels. Additionally, the microprocessor 420 controls theintensity of the LED's 302 and 304 through the LED driver 440 in a servoloop to keep the average intensity received at the photodetector 320within an appropriate range. Within the microprocessor 420 a noisereference signal n′(t) is calculated via either the constant saturationmethod or the ratiometric method, as described above, the ratiometricmethod being generally preferred. This signal is used in an adaptivenoise canceler of the joint process estimator type 60, described above.

The multiplexer 400 time multiplexes, or sequentially switches between,the electrical signals corresponding to the red and the infrared lightenergy. This allows a single channel to be used to detect and beginprocessing the electrical signals. For example, the red LED 300 isenergized first and the attenuated signal is measured at thephotodetector 320. An electrical signal corresponding to the intensityof the attenuated red light energy is passed to the common processingcircuitry. The infrared LED 302 is energized next and the attenuatedsignal is measured at the photodetector 320. An electrical signalcorresponding to the intensity of the attenuated infrared light energyis passed to the common processing circuitry. Then, the red LED 300 isenergized again and the corresponding electrical signal is passed to thecommon processing circuitry. The sequential energization of LED's 300and 302 occurs continuously while the pulse oximeter is operating.

The processing circuitry is divided into distinct paths after thesynchronized demodulator 350 to ease time constraints generated by timemultiplexing. In the preferred embodiment of the pulse oximeter shown inFIG. 10, a sample rate, or LED energization rate, of 1000 Hz isadvantageously employed. Thus, electrical signals reach the synchronizeddemodulator 350 at a rate of 1000 Hz. Time multiplexing is not used inplace of the separate paths due to settling time constraints of the lowpass filters 380, 382, and 384.

In FIG. 10, a third LED 304 is shown adjacent the finger, located nearthe LED's 300 and 302. The third LED 304 is used to measure a thirdsignal S_(λc)(t) to be used to determine saturation using theratiometric method. The third LED 304 is time multiplexed with the redand infrared LED's 300 and 302. Thus, a third signal is input to thecommon processing circuitry in sequence with the signals from the redand infrared LED's 300 and 302. After passing through and beingprocessed by the operational amplifier 330, the band pass filter 340,and the synchronized demodulator 350, the third electrical signalcorresponding to light energy at wavelength λc is input to a separatepath including a DC offset removal element 364, a first programmablegain amplifier 374, a low pass filter 384, and a second programmablegain amplifier 394. The third signal is then input to the multiplexer400.

The dashed line connection for the third LED 304 indicates that thisthird LED 304 is incorporated into the pulse oximeter when theratiometric method is used; it is unnecessary for the constantsaturation method. When the third LED 304 is used, the multiplexer 400acts as an analog switch between all three LED 300, 302, and 304signals. If the third LED 304 is utilized, feedback loops between themicroprocessor 420 and the first and second programmable gain amplifier374 and 394 in the λc wavelength path are also formed.

For pulse oximeter measurements using the ratiometric method, thesignals (logarithm converted) transmitted through the finger 310 at eachwavelength λa, λb, and λc are:

S_(λa)(t)=S_(λred1)(t)=ε_(HbO2,λa)C^(A) _(HbO2)X^(A)(t)+ε_(Hb,λa)C¹_(Hb)X^(A)(t)+ε_(HbO2,λa)C^(V) _(HbO2)X^(v)(t)+ε_(Hb,λa)C^(V)_(Hb)X^(V)(t)+n_(λa)(t).   (81)

S_(λb)(t)=S_(λred2)(t)=ε_(HbO2,λb)C^(A) _(HbO2)X^(A)(t)+ε_(Hb,λb)C^(A)_(Hb)X^(A)(t)+ε_(HbO2,λb)C^(V) _(HbO2)X^(V)(t)+ε_(Hb,λb)C^(V)_(Hb)X^(V)(t)+n_(λb)(t).   (82)

S_(λc)(t)=S_(λIR)(t)=ε_(HbO2,λc)C^(A) _(HbO2)X^(A)(t)+ε_(Hb,λc)C^(A)_(Hb)X^(A)(t)+ε_(HbO2,λc)C^(V) _(HbO2)X^(V)(t)+ε_(Hb,λc)C^(V)_(Hb)X^(V)+n_(λc)(t).   (83)

In equations (81) through (83), X^(A)(t) is the lump-sum thickness ofthe arterial blood in the finger; X^(V)(t) is the lump-sum thickness ofvenous blood in the finger; ε_(HbO2,λa) ε_(HbO2,λb), ε_(HbO2,λc),ε_(Hb,λa), ε_(Hb,λb), and ε_(Hb,λc) are the absorption coefficients ofthe oxygenated and non-oxygenated hemoglobin, at each wavelengthmeasured; and c_(HbO2)(t) and c_(Hb)(t) with the superscriptdesignations A and V are the concentrations of the oxygenated andnon-oxygenated arterial blood and venous blood, respectively.

For the ratiometric method, the wavelengths chosen are typically two inthe visible red range, i.e., λa and λb, and one in the infrared range,i.e., λc. As described above, the measurement wavelengths λa and λb areadvantageously chosen to satisfy a proportionality relationship whichremoves the desired signal portion Y_(λa)(t) and Y_(λb)(t), yielding anoise reference signal n′(t). In the preferred embodiment, theratiometric method is used to determine the noise reference signal n′(t)by picking two wavelengths that cause the desired portions Y_(λa)(t) andY_(λb)(t) of the measured signals S_(λa)(t) and S_(λb)(t) to becomelinearly dependent similarly to equation (22); i.e. wavelengths λa andλb which satisfy:

ε_(HbO2,λa)/ε_(Hb,λa)=ε_(HbO2,λb)/ε_(Hb,λb)   (84)

Typical wavelength values chosen are λa=650 nm and λb=685 nm.Additionally a typical wavelength value for λc is λc=940 nm. By pickingwavelengths λa and λb to satisfy equation (84) the venous portion of themeasured signal is also caused to become linearly dependent even thoughit is not a portion of the desired signal. Thus, the venous portion ofthe signal is removed with the desired portion. The proportionalityrelationship between equations (81) and (82) which allows determinationof a non-zero noise reference signal n′(t), similarly to equation (25)is:

ω_(r4)=ε_(Hb,λc)/ε_(Hb,λb); where   (85)

n_(λa)(t)≠ω_(r4)n_(λb)(t).   (86)

In pulse oximetry, both equations (85) and (86) can typically besatisfied simultaneously.

FIG. 11 is a graph of the absorption coefficients of oxygenated anddeoxygenated hemoglobin (ε_(HbO2) and ε_(Hb)) vs. wavelength (λ). FIG.12 is a graph of the ratio of absorption coefficients vs. wavelength,i.e., ε_(Hb)/ε_(HbO2) vs. λ over the range of wavelength within circle13 in FIG. 11. Anywhere a horizontal line touches the curve of FIG. 12twice, as does line 400, the condition of equation (84) is satisfied.FIG. 13 shows an exploded view of the area of FIG. 11 within the circle13. Values of ε_(HbO2) and ε_(Hb) at the wavelengths where a horizontalline touches the curve of FIG. 12 twice can then be determined from thedata in FIG. 13 to solve for the proportionality relationship ofequation (85).

A special case of the ratiometric method is when the absorptioncoefficients ε_(HbO2) and ε_(Hb) are equal at a wavelength. Arrow 410 inFIG. 11 indicates one such location, called an isobestic point. FIG. 13shows an exploded view of the isobestic point. To use isobestic pointswith the ratiometric method, two wavelengths at isobestic points aredetermined to satisfy equation (84).

Multiplying equation (82) by ω_(r4) and then subtracting equation (82)from equation (81), a non-zero noise reference signal n′(t) isdetermined by:

n′(t)=S_(λa)(t)−ω_(r4)S_(λb)(t)=n_(λa)(t)−ω_(r4)n_(λb).   (87)

This noise reference signal n′(t) has spectral content corresponding tothe erratic, motion-induced noise. When it is input to an adaptive noisecanceler, with either signals S_(λa)(t) and S_(λc)(t) or S_(λb)(t) andS_(λc)(t) input to two regression filters 80a and 80b, the adaptivenoise canceler will function much like an adaptive multiple notch filterand remove frequency components present in both the noise referencesignal n′(t) and the measured signals from the measured signalsS_(λa)(t) and S_(λc)(t) or S_(λb)(t) and S_(λc)(t). Thus, the adaptivenoise canceler is able to remove erratic noise caused in the venousportion of the measured signals S_(λa)(t), S_(λb)(t), and S_(λc)(t) eventhough the venous portion of the measured signals S_(λa)(t) andS_(λb)(t) was not incorporated in the noise reference signal n′(t).However, the low frequency absorption caused by venous blood movingthrough the veins is generally not one of the frequencies incorporatedinto the noise reference signal n′(t). Thus, the adaptive noise cancelergenerally will not remove this portion of the undesired signal. However,a band pass filter applied to the approximations to the desired signalsY′_(λa)(t) and Y_(λc)(t) or Y_(λb)(t) and Y′_(λc)(t) can remove thisportion of the undesired signal corresponding to the low frequencyvenous absorption.

For pulse oximetry measurements using the constant saturation method,the signals (logarithm converted) transmitted through the finger 310 ateach wavelength λa and λb are:

S_(λa)(t)=S_(λred1)(t)=ε_(HbO2,λa)C^(A) _(HbO2)X^(A)(t)+ε_(Hb,λa)C^(A)_(Hb)X^(A)(t)+ε_(HbO2,λa)C^(V) _(HbO2)X^(v)(t)+ε_(Hb,λa)C^(V)_(Hb)X^(V)(t)+n_(λa)(t).   (88)

S_(λb)(t)=S_(λIR)(t)=ε_(HbO2,λb)C^(A) _(HbO2)X^(A)(t)+ε_(Hb,λb)C^(A)_(Hb)X^(A)(t)+ε_(HbO2,λb)C^(V) _(HbO2)X^(V)(t)+ε_(Hb,λb)C^(V)_(Hb)X^(V)(t)+n_(λb)(t).   (89)

For the constant saturation method, the wavelengths chosen are typicallyone in the visible red range, i.e., λa, and one in the infrared range,i.e., λb. Typical wavelength values chosen are λa=660 nm and λb=940 nm.Using the constant saturation method, it is assumed thatC_(HbO2)(t)/C_(Hb)(t)=constant. The saturation of oxygenated arterialblood changes slowly, it at all, with respect to the sample rate, makingthis a valid assumption. The proportionality factor between equation(88) and (89) can then be written as: $\begin{matrix}{{\omega_{s4}(t)} = \frac{{\varepsilon_{{Hb02}\quad \lambda \quad a}\quad c_{Hb02}\quad x\quad (t)} + {\varepsilon_{{Hb}\quad \lambda \quad a}\quad c_{Hb}\quad x\quad (t)}}{{\varepsilon_{{Hb02}\quad \lambda \quad b}\quad c_{Hb02}\quad x\quad (t)} + {\varepsilon_{{Hb}\quad \lambda \quad b}\quad c_{Hb}\quad x\quad (t)}}} & (90) \\{\quad {{\approx {Y_{\lambda \quad a}^{\prime}\quad (t)\text{/}Y_{\lambda \quad b}^{\prime}\quad (t)}};{where}}} & (91) \\{{n_{\lambda \quad a}\quad (t)} \neq {\omega_{s4}\quad (t)\quad n_{\lambda \quad b}\quad {(t).}}} & (92)\end{matrix}$

In pulse oximetry, it is typically the case that both equation (91) and(92) can be satisfied simultaneously.

Multiplying equation (89) by ω_(s4)(t) and then subtracting equation(89) from equation (88), a non-zero noise reference signal n′(t) isdetermined by:

n′(t)=  (93)

S_(λa)(t)−ω_(S4)(t)S_(λb)(t)=ε_(HbO2,λa)c^(V)_(HbO2)x^(V)(t)+ε_(Hb,λa)c^(V)_(Hb)x^(V)(t)+n_(λa)(t)−ω_(s4)[ε_(HbO2,λb)c^(V)_(HbO2)x^(V)(t)+ε_(Hb,λb)c^(V) _(Hb)x^(V)(t)+n_(λb)(t)].   (94)

The constant saturation assumption does not cause the venouscontribution to the absorption to be canceled along with the desiredsignal portions Y_(λa)(t) and Y_(λb)(t), as did the relationship ofequation (84) used in the ratiometric method. Thus, frequenciesassociated with both the low frequency modulated absorption due tovenous absorption when the patient is still and the erraticallymodulated absorption due to venous absorption when the patient is movingare represented in the noise reference signal n′(t). Thus, the adaptivecanceler can remove both erratically modulated absorption due to venousblood in the finger under motion and the constant low frequency cyclicabsorption of venous blood.

Using either method, a noise reference signal n′(t) is determined by theprocessor of the present invention for use in an adaptive noise cancelerwhich is defined by software in the microprocessor. The preferredadaptive noise canceler is the joint process estimator 60 describedabove.

Illustrating the operation of the ratiometric method of the presentinvention, FIGS. 14, 15 and 16 show signals measured for use indetermining the saturation of oxygenated arterial blood using areference processor of the present invention which employs theratiometric method, i.e., the signals S_(λa)(t)=S_(λred1)(t),S_(λb)(t)=S_(λred2)(t), and S_(λc)(t)=S_(λIR)(t). A first segment 14a,15a, and 16a of each of the signals is relatively undistributed bymotion artifact, i.e., the patient did not move substantially during thetime period in which these segments were measured. These segments 14a,15a, and 16a are thus generally representative of the describedplethysmographic waveform at each of the measured wavelengths. A secondsegment 14b, 15b and 16b of each of the signals is affected by motionartifact, i.e., the patient did move during the time period in whichthese segments were measured. Each of these segments 14b, 15b, and 16shows large motion induced excursions in the measured signal. A thirdsegment 14c, 15c, and 16c of each of the signals is again relativelyunaffected by motion artifact and is thus generally representative ofthe desired plethysmographic waveform at each of the measuredwavelengths.

FIG. 17 shows the noise reference signal n′(t)=n_(λa)−ω_(r4)n_(λb)(t),as determined by a reference processor of the present inventionutilizing the ratiometric method. As discussed previously, the noisereference signal n′(t) is correlated to the undesired signal portionsn_(λa), n_(λb), and n_(λc). Thus, a first segment 17a of the noisereference signal n′(t) is generally flat, corresponding to the fact thatthere is very little motion induced noise in the first segments 14a,15a, and 16a of each signal. A second segment 17b of the noise referencesignal n′(t) exhibits large excursions, corresponding to the largemotion induced excursions in each of the measured signals. A thirdsegment 17c of the noise reference signal n′(t) is generally flat, againcorresponding to the lack of motion artifact in the third segments 14a,14b, and 14c of each measured signal.

FIGS. 18 and 19 show the approximation Y′_(λa)(t) and Y′_(λc)(t) to thedesired signals Y_(λa)(t) and Y_(λc)(t) as estimated by the jointprocess estimator 60 using a noise reference signal n′(t) determined bythe ratiometric method. Note that the scale of FIGS. 14 through 19 isnot the same for each figure to better illustrate changes in eachsignal. FIGS. 18 and 19 illustrate the effect of the joint processestimator adaptive noise canceler using the nose reference signal n′(t)as determined by the reference processor of the present invention usingthe ratiometric method. Segments 18b and 19b are not dominated by motioninduced noise as were segments 14b, 15b, and 16b of the measuredsignals. Additionally, segments 18a, 19a, 18c, and 19c have not beensubstantially changed from the measured signal segments 14a, 15a, 16a,14c, 15c, and 16c where there was no motion induced noise.

Illustrating the operation of the constant saturation method of thepresent invention. FIGS. 20 and 21 show signals measured for input to areference processor of the present invention which employs the constantsaturation method, i.e., the signals S_(λa)(t)=S_(λred1)(t) andS_(λb)(t)=S_(λIR)(t). A first segment 20a and 21a of each of the signalsis relatively undistributed by motion artifact, i.e., the patient didnot move substantially during the time period in which these segmentswere measured. These segments 20a and 21a are thus generallyrepresentative of the desired plethysmographic waveform at each of themeasured wavelengths. A second segment 20b and 21b of each of thesignals is affected by motion artifact, i.e., the patient did moveduring the time period in which these segments were measured. Each ofthese segments 20b and 21b shows large motion induced excursions in themeasured signal. A third segment 20c and 21c of each of the signals isagain relatively unaffected by motion artifact and is thus generallyrepresentative of the desired plethysmographic waveform at each of themeasured wavelengths.

FIG. 22 shows the noise reference signaln′(t)=n_(λa)(t)−ω_(s4)n_(λb)(t), as determined by a reference processorof the present invention utilizing the constant saturation method.Again, the noise reference signal n′(t) is correlated to the undesiredsignal portions n_(λa) and n_(λb). Thus, a first segment 22a of thenoise reference signal n′(t) is generally flat, corresponding to thefact that there is very little motion induced noise in the firstsegments 20a and 21a of each signal. A second segment 22b of the noisereference signal n′(t) exhibits large excursions, corresponding to thelarge motion induced excursions in each of the measured signals. A thirdsegment 22c of the noise reference signal n′(t) is generally flat, againcorresponding to the lack of motion artifact in the third segments 20band 21c of each measured signal.

FIGS. 23 and 24 show the approximations Y′_(λa)(t) and Y′_(λb)(t) to thedesired signals Y′_(λa)(t) and Y′_(λb)(t) as estimated by the jointprocess estimator 60 using a noise reference signal n′(t) determined bythe constant saturation method. Note that the scale of FIGS. 20 and 24is not the same for each figure to better illustrate changes in eachsignal. FIGS. 23 and 24 illustrate the effect of the joint processestimator adaptive noise canceler using the noise reference signal n′(t)as determined by a reference processor of the present inventionutilizing the constant saturation method. Segments 23b and 24b are notdominated by motion induced noise as were segments 20b and 21b of themeasured signals. Additionally, segments 23a, 24a, 23c, and 24c have notbeen substantially changed from the measured signal segments 20a, 21a,20c, and 21c where there was no motion induced noise.

Method for Estimating Desired Portions of Measured Signals in a PulseOximeter

A copy of a computer program subroutine written in the C programminglanguage, calculates a noise reference signal n′(t) using theratiometric method and, using a joint process estimator 60, estimatesthe desired signal portions of two measured signals, each having anundesired portion which is correlated to the noise reference signaln′(t) and one of which was not used to calculate the noise referencesignal n′(t), is appended in Appendix A. For example,S_(λa)(t)=S_(λred1)(t)=S_(λ650nm)(t) andS_(λc)(t)=S_(λIR)(t)=S_(λ940nm)(t) can be input to the computersubroutine. One skilled in the art will realize thatS_(λa)(t)=S_(λred2)(t)=S_(λ685nm)(t) andS_(λc)(t)=S_(λIR)(t)=S_(λ940)nm(t) will also work. This subroutine isone way to implement the steps illustrated in the flowchart of FIG. 8for a monitor particularly adapted for pulse oximetry.

The program estimates the desired signal portions of two light energysignals, one preferably corresponding to light in the visible red rangeand the other preferably corresponding to light in the infrared rangesuch that a determination of the amount of oxygen available to the body,or the saturation of oxygen in the arterial blood, may be made. Thecalculation of the saturation is performed in a separate subroutine.Various methods for calculation of the oxygen saturation are known tothose skilled in the art. One such calculation is described in thearticles by G. A. Mook, et al, and Michael R. Neuman cited above. Oncethe concentration of oxygenated hemoglobin and deoxygenated hemoglobinare determined, the value of the saturation is determined similarly toequations (73) through (80) wherein measurements at times t₁ and t₂ aremade at different, yet proximate times over which the saturation isrelatively constant. For pulse oximetry, the average saturation at timet=(t₁+t₂)/2 is then determined by: $\begin{matrix}{{{Saturation}\quad (t)} = {C_{Hb02}\quad (t){{\text{/}\left\lbrack {{C_{Hb02}\quad (t)} + {C_{Hb}\quad (t)}} \right\rbrack}.}}} & (95) \\{\quad {= \frac{\varepsilon_{{Hb}\quad \lambda \quad a} - {\varepsilon_{{Hb}\quad \lambda \quad b}\quad \left( \frac{\Delta \quad Y_{\lambda \quad a}}{\Delta \quad Y_{\lambda \quad b}} \right)}}{\varepsilon_{{Hb}\quad \lambda \quad a} - \varepsilon_{{Hb02}\quad \lambda \quad a} - {\left( {\varepsilon_{{Hb}\quad \lambda \quad b} - \varepsilon_{{Hb02}\quad \lambda \quad b}} \right)\quad \left( \frac{\Delta \quad Y_{\lambda \quad a}}{\Delta \quad Y_{\lambda \quad b}} \right)}}}} & (96)\end{matrix}$

Using the ratiometric method, three signals S_(λa)(t), S_(λb)(t), andS_(λc)(t) are input to the subroutine. S_(λa)(t) and S_(λb)(t) are usedto calculate the noise reference signal n′(t). As described above, thewavelengths of light at which S_(λa)(t) and S_(λb)(t) are measured arechosen to satisfy the relationship of equation (84). Once the noisereference signal n′(t) is determined, the desired signal portionsY_(λa)(t) and Y_(λc)(t0 of the measured signals S_(λa)(t0 and S_(λc)(t)are estimated for use in calculation of the oxygen saturation.

The correspondence of the program variables to the variables defined inthe discussion of the joint process estimator is as follows:

Δ_(m)(t)=nc[].Delta

Γ_(f,m(t))=nc[].fref

Γ_(b,m)(t)=nc[].bref

f_(m)(t)=nc[].ferr

b_(m)(t)=nc[].berr

ℑ_(m)(t)=nc[].Fswsqr

β_(m)(t)=nc[].Bswsqr

γ_(m)(t)=nc[].Gamma

ρ_(m,λa)(t)=nc[].Roh_a

ρ_(m,λc)(t)=nc[].Roh_c

e_(m,λa)(t)=nc[].err_a

e_(m,λc)(t)=nc[].err_c

κ_(m,λa)(t)=nc[].K_a

κ_(m,λc)(t)=nc[].K_c

A first portion of the program performs the initialization of theregisters 90, 92, 96, and 98 and intermediate variable values as in the“INITIALIZE NOISE CANCELER” box 120 and equations (40) through (44) andequations (61), (62), (65), and (66). A second portion of the programperforms the time updates of the delay element variables 110 where thevalue at the input of each delay element variable 110 is stored in thedelay element variable 110 as in the “TIME UPDATE OF [Z⁻¹] ELEMENTS” box130.

A third portion of the program calculates the noise reference signal, asin the “CALCULATE NOISE REFERENCE (n+(t)) FOR TWO MEASURED SIGNALSAMPLES” box 140 using the proportionality constant ω_(r4) determined bythe ratiometric method as in equation (85).

A fourth portion of the program performs the zero-stage update as in the“ZERO-STAGE UPDATE” box 150 where the zero-stage forward predictionerror f_(o)(t) and the zero-stage backward prediction error b_(o)(t) areset equal to the value of the noise reference signal n′(t) justcalculated. Additionally, zero-stage values of intermediate variablesℑ₀(t) and β₀(t) (nc[].Fswsqr and nc[].Bswsqr in the program) arecalculated for use in setting register 90, 92, 96, and 98 values in theleast-squares lattice predictor 70 and the regression filters 80a and80b.

A fifth portion of the program is an iterative loop wherein the loopcounter, m, is reset to zero with a maximum of m=NC_CELLS, as in the“m=0” box 160 in FIG. 8. NC_CELLS is a predetermined maximum value ofiterations for the loop. A typical value of NC_CELLS is between 60 and80, for example. The conditions of the loop are set such that the loopiterates a minimum of five times and continues to iterate until a testfor conversion is met or m=NC_CELLS. The test for conversion is whetheror not the sum of the weighted sum of forward prediction errors plus theweighted sum of backward prediction errors is less than a small number,typically 0.00001 (i.e, ℑ_(m)(t)+β_(m)(t) ≦0.00001).

A sixth portion of the program calculates the forward and backwardreflection coefficient Γ_(m)/(t) and Γ_(m,b)(t) register 90 and 92values (nc[].fref and nc[].bref in the program) as in the “ORDER UPDATEm^(th)-STAGE OF LSL-PREDICTOR” box 170 and equations (49) and (50). Thenforward and backward prediction errors f_(m)(t) and b_(m)(t) (nc[].ferrand nc[].berr in the program) are calculated as in equations (51) and(52). Additionally, intermediate variables ℑ_(m)(t), β_(m)(t) andγ_(m)(t) (nc[].Fswsqr, nc[].Bswsqr, nc[].Gamma in the program) arecalculated, as in equations (53), (54), and (55). The first cycle of theloop uses the values for nc[0].Fswsqr and nc[0].Bswsqr calculated in theZERO-STAGE UPDATE portion of the program.

A seventh portion of the program, still within the loop, calculates theregression coefficient κ_(m,λa)(t) and ε_(m,λc)(t) register 96 and 98values (nc[].K_a and nc[].K_c in the program) in both regressionfilters, as in the “ORDER UPDATE m^(th) STAGE OF REGRESSION FILTERS(S)”box 180 and equations (57) through (68). Intermediate error signals andvariables e_(m,λa)(t), e_(m,λc)(t), ρ_(m,λa)(t), and ρ_(m,λc)(t)(nc[].err_a and nc[].err_c, nc[].roh_a, and nc[].roh_c in thesubroutine) are also calculated as in equations (58), (64), (56), and(60), respectively.

The test for convergence of the joint process estimator is performedeach time the loop iterates, analogously to the “DONE” box 190. If thesum of the weighted sums of the forward and backward prediction errorsℑ_(m)(t)+β_(m)(t) is less than or equal to 0.00001, the loop terminates.Otherwise, the sixth and seventh portions of the program repeat.

When either the convergence test is passes for m=NC_CELLS, an eightportion of the program calculates the output of the joint processestimator 60 adaptive noise canceler as in the “CALCULATE OUTPUT” box200. This output is good approximation to both of the desired signalsY′_(λa)(t) and Y′_(λc)(t) for the set of samples S_(λa)(t), S_(λb)(t),and S_(λc)(t) input to the program. After many sets of samples areprocessed by the joint process estimator, a compilation of the outputsprovides output waves which are good approximations to theplethysmographic wave at each wavelength, λa and λc.

Another copy of a computer program subroutine, written in the Cprogramming language, which calculates a noise reference signal n′(t)using the constant saturation method and, using a joint processestimator 60, estimates a good approximation to the desired signalportions of two measured signals, each having an undesired portion whichis correlated to the noise reference signal n′(t) and each having beenused to calculate the noise reference signal n′(t), is appended inAppendix B. This subroutine is another way to implement the stepsillustrated in the flowchart of FIG. 8 for a monitor particularlyadapted for pulse oximetry. The two signals are measured at twodifferent wavelengths λa and λb, where λa is typically in the visibleregion and λb is typically in the infrared region. For example, in oneembodiment of the present invention, tailored specifically to performpulse oximetry using the constant saturation method, λa=660 nm andλb=940 nm.

The correspondence of the program variables to the variables defined inthe discussion of the joint process estimator is as follows:

Δ_(m)(t)=nc[].Delta

Γ_(f,m(t))=nc[].fref

Γ_(b,m)(t)=nc[].bref

f_(m)(t)=nc[′].ferr

b_(m)(t)=nc[].berr

ℑ_(m)(t)=nc[].Fswsqr

β_(m)(t)=nc[].Bswsqr

γ_(m)(t)=nc[].Gamma

ρ_(m,λa)(t)=nc[].Roh_a

ρ_(m,λc)(t)=nc[].Roh_b

e_(m,λa)(t)=nc[].err_a

e_(m,λb)(t)=nc[].err_b

κ_(m,λa)(t)=nc[].K_a

κ_(m,λb)(t)=nc[].K_b

First and second portions of the subroutine are the same as the firstand second portions of the above described subroutine tailored for theratiometric method of determining the noise reference signal n′(t).

A third portion of the subroutine calculates the noise reference signal,as in the “CALCULATE NOISE REFERENCE (n′(t)) FOR TWO MEASURED SIGNALSAMPLES” box 140 for signals S_(λa)(t) and S_(λb)(t) using the aproportionality constant ω_(s4)(t) determined by the constant saturationmethod as in equations (90) and (91). The saturation is calculated in aseparate subroutine and a value of ω_(s4)(t) is imported to the presentsubroutine for estimating the desired portions Y_(λa)(t) and Y_(λb)(t)of the composite measured signals S_(λa)(t) and S_(λb)(t).

Fourth, fifth, and sixth portions of the subroutine are similar to thefourth, fifth, and sixth portions of the above described programtailored for the ratiometric method. However, the signals being used toestimate the desired signal portions Y_(λa)(t) and Y_(λb)(t) in thepresent subroutine tailored for the constant saturation method, areS_(λa)(t) and S_(λb)(t), the same signals that were used to calculatethe noise reference signal n′(t).

A seventh portion of the program, still within the loop begun in thefifth portion of the program, calculates the regression coefficientregister 96 and 98 values κ_(m,λa)(t) and ε_(m,λb)(5) (nc[].K_a andnc[].K_b in the program) in both regression filters, as in the “ORDERUPDATE m^(th) STAGE OF REGRESSION FILTER(S)” box 180 and equations (57)through (67). Intermediate error signals and variables ε_(m,λa)(t),e_(m,λb)(t), ρ_(m,λa)(t), and ρ_(m,λb)(t) (nc[].err_a and nc[].err_b,nc[].roh_a, and nc[].rob_b in the subroutine) are also calculated as inequations (58), (63), (56), and (59), respectively.

The loop iterates until the test for convergence is passed, the testbeing the same as described above for the subroutine tailored for theratiometric method. The output of the present subroutine is a goodapproximation to the desired signals Y′_(λa)(t) and Y′_(λb)(t) for theset of samples S_(λa)(t) and S_(λb)(t) input to the program. Afterapproximations to the desired signal portions of many sets of measuredsignal samples are estimated by the joint process estimator, acompilation of the outputs provides waves which are good approximationsto the plethysmographic wave at each wavelength, λa and λb. Theestimating process of the iterative loop is the same in eithersubroutine, only the sample values S_(λa)(t) and S_(λc)(t) or S_(λa)(t)and S_(λb)(t) input to the subroutine for use in estimation of thedesired signal portions Y_(λa)(t) and Y_(λc)(t) or Y_(λa)(t) andY_(λb)(t) and how the noise reference signal n′(t) is calculated aredifferent for the ratiometric method and the constant saturationmethods.

Independent of the method used, ratiometric or constant saturation, theapproximations to the desired signal values Y′_(λa)(t) and Y′_(λc)(t) orY′_(λa)(t) and Y′_(λb)(t) are input to a separate subroutine in whichthe saturation of oxygen in the arterial blood is calculated. If theconstant saturation method is used, the saturation calculationsubroutine also determines a value for the proportionality constantω_(s4)(t) as defined in equations (90) and (91) and discussed above. Theconcentration of oxygenated arterial blood can be found from theapproximations to the desired signal values since the desired signalsare made up to terms comprising x(t), the thickness of arterial blood inthe finger; absorption coefficients of oxygenated and de-oxygenatedhemoglobin, at each measured wavelength; and C_(HbO2)(t) and C_(HB)(t),the concentrations of oxygenated and de-oxygenated hemoglobin,respectively. The saturation is a ratio of the concentration of oneconstituent, A₅, with respect to the total concentration of constituentsin the volume containing A₅ and A₆. Thus, the thickness, x(t), isdivided out of the saturation calculation and need not be predetermined.Additionally, the absorption coefficients are constant at eachwavelength. The saturation of oxygenated arterial blood is thendetermined as in equations (95) and (96).

While one embodiment of a physiological monitor incorporating aprocessor of the present invention for determining a noise referencesignal for use in an adaptive noise canceler to remove erratic noisecomponents from a physiological measurement has been described in theform of a pulse oximeter, it will be obvious to one skilled in the artthat other types of physiological monitors may also employ the abovedescribed techniques for noise reduction on a composite measured signalin the presence of noise.

Furthermore, it will be understood that transformations of measuredsignals other than logarithmic conversion and determination of aproportionality factor which allows removal of the desired signalportions for determination of a noise reference signal are possible.Additionally, although the proportionality factor ω has been describedherein as a ratio of a portion of a first signal to a portion of asecond signal, a similar proportionality constant determined as a ratioof a portion of a second signal to a portion of a first signal couldequally well be utilized in the processor of the present invention. Inthe latter case, a noise reference signal would generally resemblen′(t)=n_(λb)(t)−ωn_(λa)(t).

It will also be obvious to one skilled in the art that for mostphysiological measurements, two wavelengths may be determined which willenable a signal to be measured which is indicative of a quantity of acomponent about which information is desired. Information about aconstituent of any energy absorbing physiological material may bedetermined by a physiological monitor incorporating a signal processorof the present invention and an adaptive noise canceler by determiningwavelengths which are absorbed primarily by the constituent of interest.For most physiological measurements, this is a simple determination.

Moreover, one skilled in the art will realize that any portion of apatient or a material derived from a patient may be used to takemeasurements for a physiological monitor incorporating a processor ofthe present invention and an adaptive noise canceler. Such areas includea digital such as a finger, but are not limited to a finger.

One skilled in the art will realize that many different types ofphysiological monitors may employ a signal processor of the presentinvention in conjunction with an adaptive noise canceler. Other types ofphysiological monitors include, but are not limited to, electroncardiographs, blood pressure monitors, blood gas saturation (other thanoxygen saturation) monitors, capnographs, heart rate monitors,respiration monitors, or depth of anesthesia monitors. Additionally,monitors which measure the pressure and quantity of a substance withinthe body such as a breathalizer, a drug monitor, a cholesterol monitor,a glucose monitor, a carbon dioxide monitor, a glucose monitor, or acarbon monoxide monitor may also employ the above described techniquesfor removal of undesired signal portions.

Furthermore, one skilled in the art will realize that the abovedescribed techniques of noise removal from a composite signal includingnoise components can also be performed on signals made up of reflectedenergy, rather than transmitted energy. One skilled in the art will alsorealize that a desired portion of a measured signal of any type ofenergy, including but not limited to sound energy, X-ray energy, gammaray energy, or light energy can be estimated by the noise removaltechniques described above. Thus, one skilled in the art will realizethat the processor of the present invention and an adaptive noisecanceler can be applied in such monitors as those using ultrasound wherea signal is transmitted through a portion of the body and reflected backfrom within the body back through this portion of the body.Additionally, monitors such as echo cardiographs may also utilize thetechniques of the present invention since they too rely on transmissionand reflection.

While the present invention has been described in terms of aphysiological monitor, one skilled in the art will realize that thesignal processing techniques of the present invention can be applied inmany areas, including but not limited to the processing of aphysiological signal. The present invention may be applied in anysituation where a signal processor comprising a detector receives afirst signal which includes a first desired signal portion and a firstundesired signal portion and a second signal which includes a seconddesired signal portion and a second undesired signal portion. The firstand second signals propagate through a common medium and the first andsecond desired signal portions are correlated with one another.Additionally, at least a portion of the first and second undesiredsignal portions are correlated with one another due to a perturbation ofthe medium while the first and second signals are propagating throughthe medium. The processor receives the first and second signals andcombines the first and second signals to generate a noise referencesignal in which the primary component is derived from the first andsecond undesired signal portions. Thus, the signal processor of thepresent invention is readily applicable to numerous signal processingareas.

/**********************************************************************************APPENDIX A************************************************Least Square Lattice**********************************************Noise Cancelling********************* /*Example for ratiometric approach to noise cancelling */ #define LAMBDA0.95 void OxiLSL_NC ( int reSet, int passes, int *signal_1, int*signal_2, int *signal_3, int *target_1, int *target_2,) { int i, ii, k,m, n, contraction; static int *s_a, *s_b, *s_c, *out_a, *out_c; staticfloat Delta_sqr, scale, noise_ref; if( reset == TRUE) { s_a = signal_1;s_b = signal_2; s_c = signal_3; out_a = target_1; out_c = target_2;factor = 1.5; scale = 1.0/4160.0; /* noise canceller initialization attiue t=0 */ nc[0].berr = 0.0; nc[0].Gamma = 1.0; for(m=0; m<NC_CELLS;m++) { nc[m].err_a = 0.0; nc[m].err_b = 0.0; nc[m].Roh_a = 0.0;nc[m].Roh_c = 0.0; nc[m].Delta = 0.0; nc[m].Fswsqr = 0.00001;nc[m].Bswsqr = 0.00001; } } /*================ END INITIALIZATION================*/ For (k=0; k<passes; k++){ contraction = FALSE;for(m=0; m<NC_CELLS; m++) { /* Update delay elements */ nc[m].berr1 =nc[m ].berr; nc[m].Bswsqr1 = nc[m].Bswsqr; } noise_ref = factor *log(1.0 − (*s_a) * scale) = log(1.0 − (*s_b) * scale) ; nc[0].err_n =log(1.0 − (*s_b) * scale); nc[0].err_b = log(1.0 − (*s_c) * scale);++s_a; ++s_b; ++s_c; nc[0].ferr = noise_ref ; nc[0].berr = noise_ref ;nc[0].Fswsqr = LAMBDA * nc[0].Fswsqr + noise_ref * noise_ref;nc[0].Bswsqr = nc[0].Fswsqr; /* Order Update */ for(n=1;( n < NC_CELLS)&& (contraction == FALSE); n++) { /* Adaptive Lattice Section */ m = n −1; ii = n − 1; nc[m].Delta *= LAMBDA; nc[m].Delta += nc[m].berr1 *nc[m].ferr / nc[m].Gamma ; Delta_sqr = nc[m].Delta * nc[m].Delta;nc[n]fref = −nc[m].Delta / nc[m].Bswsqr1; nc[n].bref = −nc[m].Delta /nc[m].Fswsqr; nc[n].ferr = nc[m].ferr + nc[n].fref * nc[m].berr1;nc[n].berr = nc[m].berr1 + nc[n].bref * nc[m].ferr; nc[n].Fswsqr =nc[m].Fswsqr − Delta_sqr / nc[m].Bswsqr1; nc[n].Bswsqr = nc[m].Bswsqr1 −Delta_sqr / nc[m].Fswsqr; if( (nc[n].Fswsqr + nc[n].Bswsqr) > 0.00001 ∥(n < 5) ) { nc[n].Gamma = nc[m].Gamma − nc[m].berr1 *  nc[m].berr1 /nc[m].Bswsqr1; if(nc[n].Gamma < 0.05) nc[n].Gamma = 0.05;if(nc[n].Gamma > 1.00) nc[n].Gamma = 1.00; /* Joint Process EstimationSection */ nc[m].Roh_a *= LAMBDA; nc[m].Roh_a += nc[m].berr *nc[m].err_a / nc[m].Gamma ; nc[m].k_a  = nc[m].Roh_a / nc[m].Bswsqr;nc[n].err_a  = nc[m].err_a − nc[m].k_a * nc[m].berr; nc[m].Roh_c *=LAMBDA; nc[m].Roh_c += nc[m].berr* nc[m].err_b / nc[m].Gamma; nc[m].k_c = nc[m].Roh_c / nc[m].Bswsqr; nc[n].err_b  = nc[m].err_b − nc[m].k_c *nc[m].berr; } else { contraction = TRUE; for(i=n; i<NC_CELLS; i++) {nc[i].err_a = 0.0; nc[i].Roh_a = 0.0; nc[i].err_b = 0.0; nc[i].Roh_c =0.0; nc[i].Delta = 0.0; nc[i].Fswsqr = 0.00001; nc[i].Bswsqr = 0.00001;nc[i].Bswsqr1 = 0.00001; } } } *out_a++ = (int) ((−exp(nc[ii].err_a)+1.0) / scale) ; *out_c++ = (int) ((−exp(nc[ii].err_b) +1.0) / scale) ;} } /******************* Least Square Lattice ******************************************        ***********************************************************************************/

/********************************************************************************* APPENDIX B ********************************************* Least Square Lattice ***********************************************Noise Cancelling ************************/ /*Example for constant saturation approach to noise cancelling */ #defineLAMBDA 0.95 void OxilSL_NC ( int reset, int passes, int sat_factor,int *signal_1, int signal_2, int target_1, int target_2) { int i, ii, k,m, n, contraction; static int *s_a, *s_b, *s_c, *out_b; static intDelta_sqr, scale, noise_ref; if( reset == TRUE){ s_a = signal_1; s_b =signal_2; out_a = target_1; out_b = target_2; scale = 1.0/4160.0;/*noise canceller initialization at time t=0 */ nc[0].berr = 0.0;nc[0].Gamma = 1.0; for(m=0; m<NC_CELLS; m++) { nc[m].err_a = 0.0;nc[m].err_b = 0.0; nc[m].Roh_a = 0.0; nc[m].Roh_b = 0.0; nc[m].Delta =0.0; nc[m].Fswsqr = 0.00001; nc[m].Bswsqr = 0.00001; } }/*================ END INITIALIZATION ================*/ For (k=0;k<passes; k++) { contraction = FALSE; for(m=0; ms<NC_CELLS; m++){  /*Update delay elements */ nc[m].berr1 = nc[m].berr; nc[m].Bswsqr1 =nc[m].Bswsqr; } noise_ref = sat_factor * log(1.0 − (*s_a) * scale) −log(1.0 − (*s_b) * scale) ; nc[0].err_a = log(1.0 − (*s_a) * scale);nc[0].err_b = log(1.0 − (*s_b) * scale); ++s_a; ++s_b; nc[0].ferr =noise_ref ; nc[0].berr = noise_ref ; nc[0].Fswsqr = LAMBDA *nc[0].Fswsqr + noise_ref * noise_ref; nc[0].Bswsqr = nc[0].Fswsqr; /*Order Update */ for(n=1;( n < NC_CELLS) && (contraction == FALSE); n++){ /* Adaptive Lattice Section */ m = n−1; ii = n−1; nc[m].Delta *=LAMBDA; nc[m].Delta += nc[m].berr1 * nc[m].ferr / nc[m].Gamma ;Delta_sqr  = nc[m].Delta * nc[m].Delta; nc[n].fref  = −nc[m].Delta /nc[m].Bswsqr1; nc[n].bref  = −nc[m].Delta / nc[m].Fswsqr; nc[n].ferr  =nc[m].ferr + nc[n].fref * nc[m].berr1; nc[n].berr  = nc[m].berr1 +nc[n].bref * nc[m].ferr; nc[n].Fswsqr  = nc[m].Fswsqr − Delta_sqr /nc[m].Bswsqr1; nc[n].Bswsqr  = nc[m].Bswsqr1 − Delta_sqr / nc[m].Fswsqr;if( (nc[n].Fswsqr + nc[n].Bswsqr) > 0.00001 ∥ (n < 5) ) { nc[n].Gamma =nc[m].Gamma − nc[m].berr1 *  nc[m].berr1 / nc[m].Bswsqr1; if(nc[n].Gamma< 0.05) nc[n].Gamma = 0.05; if(nc[n].Gamma > 1.00) nc[n].Gamma = 1.00;/* Joint Process Estimation Section */ nc[m].Roh_a *= LAMBDA;nc[m].Roh_a += nc[m]berr * nc[m].err_a / nc[m].Gamma ; nc[m].k_a  =nc[m].Roh_a / nc[m].Bswsqr; nc[m].err_a  = nc[m]err_a − nc[m].k_a *nc[m].berr; nc[m].Roh_b *= LAMBDA; nc[m].Roh_b += nc[m]berr *nc[m].err_b / nc[m].Gamma ; nc[m].k_b  = nc[m].Roh_b / nc[m].Bswsqr;nc[n].err_b  = nc[m].err_b − nc[m].k_b * nc[m].berr; } else {contraction = TRUE; for(i=n; i<NC_CELLS; i++) { nc[i].err_a = 0.0;nc[i].Roh_a = 0.0; nc[i].err_b = 0.0; nc[i].Roh_b = 0.0; nc[i].Delta =0.0; nc[i].Fswsqr = 0.00001; nc[i].Bswsqr = 0.00001; nc[i].Bswsqr1 =0.00001; } } } *out_a++ = (int) ((−exp(nc[ii].err_a) +1.0) / scale) ;*out_b++ = (int) ((−exp(nc[ii].err_b) +1.0) / scale) ; } }/******************* Least Square Lattice ******************************************        ***********************************************************************************/

What is claimed is:
 1. A method of determining an indication of bloodoxygen saturation comprising the steps of: transmitting light of atleast first and second wavelengths through body tissue carrying blood toa light-sensitive detector to generate first and second measuredintensity signals; filtering at least one of said first and secondintensity signals with an adaptive canceler to provide at least oneoutput signal; and calculating oxygen saturation based upon said atleast one output signal.
 2. The method of claim 1, wherein said step oftransmitting light comprises the steps of transmitting a firstwavelength in the red wavelength range and a second wavelength in theinfrared wavelength range.
 3. The method of claim 2, wherein said firstand said second signals have at least a desired physiological componentand an artifact component.
 4. The method of claim 3, wherein said firstand second wavelengths are selected based on light absorptioncharacteristics of the physiologic medium, such that a substantiallylinear relationship exists between the desired physiologic components ofsaid first and second measured signals.
 5. The method of claim 1,further comprising the step of converting said first and secondintensity signals to a digital representation of said first and secondintensity signals, and wherein said step of filtering at least one ofsaid first and second intensity signals with said adaptive cancelercomprising filtering said digital representation.
 6. The method of claim1, further comprising the step of filtering said first and secondsignals with a predetermined filter prior to said filtering at least oneof said first and second intensity signals with an adaptive canceler. 7.The method of claim 6, further comprising the step of converting saidfirst and second intensity signals to a digital representation of saidfirst and second intensity signals, and wherein said step of filteringat least one of said first and second intensity signals with an adaptivecanceler comprises filtering said digital representation.
 8. The methodof claim 6, further comprising the step of displaying said oxygensaturation on a display.
 9. The method of claim 1, further comprisingthe step of displaying said oxygen saturation on a display.
 10. Themethod of claim 1, wherein said step of filtering at least one of saidfirst and second intensity signals with an adaptive canceler comprisesthe steps of: multiplying at least one of said first and secondintensity signals by a predetermined constant and subtracting the resultfrom the other of said first and second intensity signals to provide areference signal; and filtering at least one of said first and secondintensity signals based upon said reference signal.
 11. The method ofclaim 5, wherein said step of filtering at least one of said first andsecond intensity signals with an adaptive canceler comprises the stepsof: multiplying at least one of the digital representations of saidfirst and second intensity signals by a predetermined constant andsubtracting the result from the other of said first and second intensitysignals to provide a reference signal; and adaptively filtering at leastone of the digital representations of said first and second intensitysignals based upon said reference signal.
 12. The method of claim 11,further comprising the step of filtering said first and second signalswith a predetermined filter prior to filtering at least one of saidfirst and second intensity signals with an adaptive canceler.
 13. Themethod of claim 5, where said adaptive canceler is a dynamic multiplenotch filter.
 14. The method of claim 13, wherein said adaptive canceleradjusts its transfer function in accordance with a predeterminedalgorithm.
 15. The method of claim 14, wherein said predeterminedalgorithm is a least-squares algorithm.
 16. A pulse oximeter whichmeasures the oxygen saturation of blood in body tissue, said pulseoximeter comprising: a light emitter adapted to emit light of at leastfirst and second wavelengths; a light detector responsive to light fromsaid light emitter which has passed through body tissue having blood,said light detector providing intensity signals; an adaptive filterresponsive to said intensity signals to provide at least one filteredsignal; and a oxygen saturation module responsive to at least saidfiltered signal to calculate oxygen saturation of said blood.
 17. Thepulse oximeter of claim 16, further comprising a display coupled to saidoxygen saturation module.
 18. The pulse oximeter of claim 16, whereinsaid adaptive filter comprises a first predetermined filter and adaptivecorrelation canceler an adaptive noise canceler.
 19. The pulse oximeterof claim 16, further comprising an analog to digital converter incommunication with said light detector, said analog to digital converterproviding digital representations of said intensity signals, said analogto digital converter providing said digital representations to saidadaptive filter.
 20. The pulse oximeter of claim 19, further comprisinga signal conditioner coupled between said light detector and said analogto digital converter.
 21. The pulse oximeter of claim 16 18, whereinsaid adaptive filternoise canceler is coupled to comprises amultiplication unit and an adaptive correlation noise canceler .
 22. Thepulse oximeter of claim 21 wherein said adaptive filter noise cancelerfurther comprises a predetermined filter.
 23. The pulse oximeter ofclaim 16, wherein said adaptive filter is a dynamic multiple notchfilter.
 24. The pulse oximeter of claim 23, wherein said adaptive filteradjusts its transfer function in accordance with a predeterminedalgorithm.
 25. The pulse oximeter of claim 24, wherein saidpredetermined algorithm is a least squares lattice.
 26. A pulse oximeterwhich measures the oxygen saturation of blood in body tissue, said pulseoximeter comprising: a light emitter adapted to emit light of at leastfirst and second wavelengths; a light detector responsive to light fromsaid light emitter which has passed through body tissue having blood,said light detector providing intensity signals; a digital to analogconverter which digitizes the intensity signals from said lightdetector; a multiple notch filter responsive to said intensity signalsafter conversion with said digital to analog converter to provide atleast one filtered signal; and an oxygen saturation module responsive toat least said filtered signal to calculate oxygen saturation of saidblood.
 27. The method of claim 26, wherein said multiple notch filteradjusts its transfer function based on a predetermined algorithm.
 28. Apulse oximeter which measures the oxygen saturation of blood in bodytissue, said pulse oximeter comprising: a light emitter adapted to emitlight of at least first and second wavelengths; a light detectorresponsive to light from said light emitter which has passed throughbody tissue having blood, said light detector providing intensitysignals having desired and undesired signal portions; an analog todigital converter which digitizes the intensity signals from said lightdetector; an adaptive signal processor responsive to that operates toprocess said intensity signals to adaptively filter said intensitysignals to provide processed intensity signals; and an oxygen saturationmodule routine responsive to at least one signal said processedintensity signals to calculate oxygen saturation of said blood.
 29. Thepulse oximeter of claim 28, wherein said adaptive signal processorcomprises an adaptive noise canceler.
 30. The pulse oximeter of claim29, wherein said adaptive noise canceler comprises a joint processestimator with a least-squares lattice predictor.
 31. The pulse oximeterof claim 29, wherein said adaptive noise canceler operates as a multiplenotch filter.
 32. The pulse oximeter of claim 28, wherein said adaptivesignal processor comprises an adaptive filter.
 33. A method fordetermining oxygen saturation of blood in body tissue, the methodcomprising the steps of: emitting light of at least first and secondwavelengths; detecting the light of at least first and secondwavelengths that has passed through body tissue including pulsing bloodto produce at least one intensity signal; processing a representation ofthe at least one intensity signal using an adaptive algorithm to provideat least one output signal; and calculating an oxygen saturation of thepulsing blood using the at least one output signal.
 34. The method ofclaim 33, wherein the representation of the at least one intensitysignal is a digital representation.
 35. The method of claim 33, furthercomprising the step of displaying the calculated oxygen saturation ofthe blood.
 36. The method of claim 33, wherein the step of processingcomprises processing the representation using a component of an adaptivenoise canceler.
 37. The method of claim 33, wherein the adaptivealgorithm is a least squares algorithm.
 38. The method of claim 33,wherein the adaptive algorithm is a least mean square algorithm.
 39. Apulse oximeter comprising: light emitters that emit light of at leastfirst and second wavelengths; a light detector responsive to the lightfrom the light emitters that has passed through body tissue includingpulsing blood, the light detector providing at least one intensitysignal; an analog to digital converter that provides a digitalrepresentation of the at least one intensity signal; a processorincluding a first routine to adaptively process the digitalrepresentation of the at least one intensity signal to provide at leastone output signal; and a second routine responsive to the at least oneoutput signal to calculate oxygen saturation of the blood.
 40. The pulseoximeter of claim 39, wherein the first routine comprises an adaptivealgorithm.
 41. The pulse oximeter of claim 40, wherein the adaptivealgorithm comprises a least squares algorithm.
 42. The pulse oximeter ofclaim 40, wherein the adaptive algorithm comprises a least mean squarealgorithm.
 43. The pulse oximeter of claim 41, wherein the adaptivealgorithm comprises a least squares lattice algorithm.
 44. The pulseoximeter of claim 39, wherein the processor comprises a component of anadaptive noise canceler.